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+*** START OF THE PROJECT GUTENBERG EBOOK 44371 ***
+
+Transcriber's Notes:
+
+Text between underscores represents _italics_, small capitals have been
+transcribed as ALL CAPITALS.
+
+Curly brackets indicate {subscripts}; letters between square brackets
+(such as [T] and [U]) represent the shape rahter than the letter itself.
+
+More Transcriber's Notes may be found at the end of this text.
+
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+  BY
+
+  WILLIAM HENRY THORPE
+  ASSOC. M. INST. C. E.
+
+  WITH 103 ILLUSTRATIONS
+
+  [Illustration]
+
+  London
+  E. & F. N. SPON, LIMITED, 57 HAYMARKET
+  New York
+  SPON & CHAMBERLAIN, 123 LIBERTY STREET
+
+  1906
+
+
+
+
+PREFACE
+
+
+In offering this little book to the reader interested in Bridgework, the
+author desires to express his acknowledgments to the proprietors of
+“Engineering,” in which journal the papers first appeared, for their
+courtesy in facilitating the production in book form.
+
+It may possibly happen that the scanning of these pages will induce
+others to observe and collect information extending our knowledge of
+this subject--information which, while familiar to maintenance engineers
+of experience, has not been so readily available as is desirable.
+
+No theory which fails to stand the test of practical working can
+maintain its claims to regard; the study of the behaviour of old work
+has, therefore, a high educational value, and tends to the occasional
+correction of views which might otherwise be complacently retained.
+
+  60 WINSHAM STREET,
+  CLAPHAM COMMON, LONDON, S.W.
+  _October_, 1906.
+
+
+
+
+CONTENTS
+
+
+  CHAPTER I.
+
+  INTRODUCTION--GIRDER BEARINGS.
+
+                                                                    PAGE
+
+  Pressure distribution--Square and skew bearings--Fixed bearings--
+  Knuckles--Rollers--Yield of supports                                 1
+
+
+  CHAPTER II.
+
+  MAIN GIRDERS.
+
+  _Plate webs_: Improper loading of flanges--Twisting of girders--
+  Remedial measures--Cracks in webs--Stiffening of webs--[T]
+  stiffeners                                                           9
+
+  _Open webs_: Common faults--Top booms--Buckling of bottom booms--
+  Counterbracing--Flat members                                        17
+
+
+  CHAPTER III.
+
+  BRIDGE FLOORS.
+
+  Liability to defects--Impact--Ends of cross and longitudinal
+  girders--Awkward riveting--Fixed ends to cross girders--Plated
+  floor--Liberal depths desirable--Type connections--Effect of “skew”
+  on floor--Water-tightness--Drainage--Timber floors--Jack arches--
+  Corrugated sheeting--Ballast--Rail joints--Effect of main girders
+  on floors                                                           20
+
+
+  CHAPTER IV.
+
+  BRACING.
+
+  Effect of bracing on girders--Influence of skew on bracing--Flat
+  bars--Overhead girders--Main girders stiffened from floor--
+  Stiffening of light girders--Incomplete bracing--Tall piers--Sea
+  piers                                                               34
+
+
+  CHAPTER V.
+
+  RIVETED CONNECTIONS.
+
+  Latitude in practice--Laboratory experiments--Care in considering
+  practical instances--Main girder web rivets--Lattice girders
+  investigated--Rivets in small girders--Faulty bridge floor--
+  Stresses in rivets--Cross girder connections--Tension in rivets--
+  Defective rivets--Loose rivets--Table of actual rivet stresses--
+  Bearing pressure--Permissible stresses--Proposed table--Immunity of
+  road bridges from loose rivets--Rivet spacing                       45
+
+
+  CHAPTER VI.
+
+  HIGH STRESS.
+
+  Elastic limit--Care in calculation--Impact--Examples of high stress
+  --Early examples of high stress in steel girders--Tabulated
+  examples--General remarks                                           61
+
+
+  CHAPTER VII.
+
+  DEFORMATIONS.
+
+  Various kinds--Flexing of girder flanges--Examples--Settlement
+  deformations--Creeping--Temperature changes--Local distortions--
+  Imperfect workmanship--Deformation of cast-iron arches              73
+
+
+  CHAPTER VIII.
+
+  DEFLECTIONS.
+
+  Differences as between new work and old--Influence of booms and web
+  structure on deflection--Yield of rivets and stiffness of
+  connections--Working formulæ--Set--Effect of floor system--
+  Deflection diagrams--Loads quickly applied--“Drop” loads--Flexible
+  girders--Measuring deflections--New method of observing deflections
+  --Effect of running load                                            85
+
+
+  CHAPTER IX.
+
+  DECAY AND PAINTING.
+
+  Examples of rusting of wrought-iron girders--Girder over sea-water
+  --Rate of rusting--Steelwork--Precautions--Red-lead--Repainting--
+  Scraping--Girders built into masonry--Cast iron--Effect of sea-
+  water on cast iron--Examples--Tabulated observations--Percentage of
+  submersion--Quality of metal                                        96
+
+
+  CHAPTER X.
+
+  EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+  Purpose--Methods of examination--Calculations--Stress in old work--
+  Methods of reducing stress--Repair--Loose rivets--Replacing wasted
+  flange plates--Adding new to old sections--Principles governing
+  additions--Example--Strengthening lattice girder bracings--Bracing
+  between girders--Strengthening floors--Distributing girders        107
+
+
+  CHAPTER XI.
+
+  STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+  Principal methods in use--Method of calculation--Adjustments--
+  Connections--Method of execution--Checks--Effect of skew on method
+  considered--Results of calculation for a typical case--Probable
+  error--Practical examples--Special case--Method of determining
+  flexure curves                                                     122
+
+
+  CHAPTER XII.
+
+  CAST-IRON BRIDGES.
+
+  Limitations of cast iron--Stress examples--Advantages and
+  disadvantages--Foundry stresses--Examples--Want of ductility of
+  cast iron--Repairs--Restricted possibilities                       141
+
+
+  CHAPTER XIII.
+
+  TIMBER BRIDGES.
+
+  Perishable nature--Causes of decay--Sag--Lateral bracing--Piles--
+  Uncertainty respecting decay--Examples--Conditions and practice
+  favourable to durability--Bracing--Protection--Repair--Piles--Cost 149
+
+
+  CHAPTER XIV.
+
+  MASONRY BRIDGES.
+
+  Definition--Cause of defects or failure--Spreading of abutments--
+  Closing in--Example--Stop piers--Example of failure--Strength of
+  rubble arch--Equilibrium of arches--Effect of vibration on masonry
+  --Safety centring--Methods of repair--Pointing--Rough dressed
+  stonework                                                          157
+
+
+  CHAPTER XV.
+
+  LIFE OF BRIDGES--RELATIVE MERITS.
+
+  Previous history--Causes of limited life--Tabulated examples of
+  short-lived metallic bridges--Timber and masonry bridges--
+  Durability--Maintenance charges--First cost--Comparative merits--
+  Choice of material                                                 165
+
+
+  CHAPTER XVI.
+
+  RECONSTRUCTION AND WIDENING OF BRIDGES.
+
+  CONCLUSION.
+
+  Measuring up--Railway under-bridges--Methods of reconstruction in
+  common use--Reconstruction of bridges of many openings--Timber
+  staging--Traffic arrangements--Sunday work--Railway over-bridges--
+  Widenings--Junction of new and old work--Concluding remarks--Study
+  of old bridgework                                                  172
+
+  INDEX                                                              187
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK.
+
+
+
+
+CHAPTER I.
+
+INTRODUCTION.
+
+
+No book has, so far as the author is aware, been written upon that
+aspect of bridgework to be treated in the following pages. No excuse
+need, therefore, be given for adding to the already large amount of
+published matter dealing with bridges. Indeed, as it too often happens
+that the designing of such constructions, and their after-maintenance,
+are in this country entirely separated, it cannot but be useful to give
+such results of the behaviour of bridges, whether new or old, as have
+come under observation.
+
+In the early days of metallic bridges there was of necessity no
+experience available to guide the engineer in his endeavour to avoid
+objectionable features in design, and he was, as a result, compelled to
+rely upon his own foresight and judgment in any attempt to anticipate
+the effects of those influences to which his work might later be
+subject. How heavily handicapped he must have been under these
+conditions is evident from the mass of information since acquired by the
+experimental study of the behaviour of metals under stress, and the
+growth of the literature of bridgework during the last forty years. That
+many mistakes were made is little occasion for surprise; rather is it a
+cause for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the study of defects
+and failures, even though they be of such a character that no
+experienced designer would now furnish like examples.
+
+Modern instances may, none the less, be found, with faults repeated,
+which should long since have disappeared from all bridgework, and are
+only to be accounted for by the unnatural divorce of design and
+maintenance already referred to. As the reader proceeds, it may appear
+that details are occasionally touched upon of a character altogether too
+crude and objectionable to need comment; but the consideration of these
+cases is none the less interesting, and, so far as the author’s
+observation goes, not altogether unnecessary.
+
+Most of the instances cited are of bridges, or parts of bridges, of
+quite small dimensions; but it is these which most commonly give
+trouble, both because the effects of impact are in such cases most
+severely felt, and possibly because the smaller class of bridges is very
+generally designed by men of less experience, than large and imposing
+structures.
+
+The particulars given relate in all cases to bridges of wrought iron,
+unless otherwise described.
+
+An endeavour has been made to secure some kind of order in dealing with
+the subject, but it has been found difficult to avoid a somewhat
+disjointed treatment, inseparable, perhaps, from the nature of the
+matter. Finally, the reader may be assured that every case quoted has
+come under the writer’s personal notice.
+
+
+GIRDER BEARINGS.
+
+In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing allowed. Clearly,
+the surface over which the pressure is distributed should be
+sufficiently ample to avoid overloading and possible crushing or
+fracture of bedstones where these exist; but if no knuckles are
+introduced, this is an extremely difficult matter to insure. A long
+bearing may deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.
+
+If the girder is made with truly level bearings, and the beds set level,
+it will certainly, when under load, throw an extreme pressure upon that
+part of the bearing surface immediately under the forward edge of the
+bearing-plate. These considerations probably account for bedstones
+frequently cracking, in addition to which possibility there is the
+disadvantage that the designer does not know where the girder will rest,
+and cannot truly define the span. The variation of flange-stress due to
+this cause may, in a girder of ordinary proportions, having bearings
+equal in length to the girder’s depth, be as much as 15 per cent. above
+or below that intended.
+
+If great care be taken in setting beds, in the first instance, to dip
+toward the centre of the span an amount depending upon the anticipated
+girder deflection, it may be possible to insure that when under full
+load the girder bearing shall rest equally upon its seat; but this is
+evidently a difficult condition to obtain practically, is good only for
+one degree of loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence of a
+slight leaning forward of abutment walls.
+
+Double or treble thicknesses of hair-felt are sometimes placed beneath
+girder bearings, with the object of securing a better distribution of
+pressure, no doubt with advantage; but this practice, though it may be
+quite satisfactory as applied to girders carrying an unchangeable load,
+hardly meets the case for loads which are variable. Notwithstanding the
+faulty nature of the plain bearing ordinarily used for girders of
+moderate span, its extreme simplicity commends it to most engineers. It
+must be admitted that no serious inconvenience need be anticipated in
+the majority of cases, particularly if the bearings are limited in
+length, do not approach nearer than 3 inches to the face of bedstones,
+and are furnished with hair-felt or similar packing.
+
+[Illustration: FIG. 1.]
+
+Whether with long or short bearings, the forward edge should be at right
+angles to the girder’s length. In skew bridges it is sometimes seen that
+this edge follows the angle of skew. The effect on the girder is to
+twist it, as will be clear from a little consideration. In evidence of
+this the case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment right up to the
+masonry face at a rather bad angle (about 15 degrees), was, after twenty
+years, found canted over at the top to the extent of 4 inches, with the
+further result of springing a joint in the top flange at about the
+middle of the girder, causing some rivets to loosen. The bedstone was
+also very badly broken at the face, and had to be replaced in the course
+of repairs (Fig. 1). This girder had, in addition to the canting from
+the upright position at its end, and the distortion of the top flange, a
+curvature in the same direction, though less in amount, at the
+bottom--an effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder end to creep
+along the abutment away from the point at which it bears hardest, under
+frequent applications and removals of the live load, and accompanying
+deflections.
+
+This tendency to travel may be aggravated in bridges carrying a
+ballasted road, in which there may be a considerable thickness of
+ballast near the bearings, by the compacting and spreading of this
+material taking effect upon the girder end, tending to push it outwards,
+being tied only by a few light cross-girders badly placed for useful
+effect. The movement may be prevented in new work for moderate angles of
+skew by carrying the end cross-girders well back, and securing them in
+some efficient manner; or by the introduction of a diagonal tie
+following the skew face, and attached to cross and main girder flanges
+(Fig. 2)--a method which may be applied to existing work also.
+
+[Illustration: FIG. 2.]
+
+For such a case as that cited it is imperative that ballast pressure at
+the girder end should be altogether eliminated.
+
+The fixing of girder ends by bolts--a practice at one time usual--hardly
+calls for remark, as it is now seldom resorted to unless for special
+reasons; but it may be well to point out the weakening effect of holes
+for any purpose in bedstones. Bed-plates commonly need no fixing; the
+weight carried keeps them in position, or if, in the case of very light
+girders upon separate plates, it is considered well to secure these from
+shifting, it may best be done by letting the plate in bodily a small
+amount, or by means of a very shallow feather sunk into a chase.
+
+[Illustration: FIG. 3.]
+
+As an improvement upon the plain bearing usually adopted, it is an easy
+matter so to design girder-ends as to deliver the load by a narrow strip
+of bearing-plate carried across the bottom flange, distributing the
+pressure upon the stone, if there be one, by means of a simple
+rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle
+will by this means result, with freedom to slide, and the girder span be
+defined within narrow limits. A true knuckle is, of course, the best
+means of securing imposition of the load always in the same place; but
+this by itself is not sufficient where the girder is of a length to make
+temperature and stress variations important, in which case rollers, or
+freedom to slide, become necessary. Bridges exist in which
+roller-bearings have been adopted without the knuckle, or its
+equivalent, but this is wholly indefensible, as it is obvious that the
+forward roller will in all probability take the whole load, and cannot
+be expected to keep its shape and roll freely under this mal-treatment.
+It is sometimes asserted that rollers are never effective after some
+years’ use; that they become clogged with dirt, and refuse to perform
+their office.
+
+There is no reason why rollers should not be boxed in to exclude dirt by
+a casing easily removed, some attention being given to them, and any
+possible accumulation of dirt removed each time the bridge is painted.
+
+To test the behaviour of rollers under somewhat unfavourable conditions
+for their proper action--that of the bearings of main roof trusses of
+crescent form, 190 feet span--the author, some thirty years since, took
+occasion to make the necessary observations, and found evidence of a
+moderate roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders resting upon
+columns, particularly if of cast iron, a roller and knuckle arrangement
+is most desirable for any but very small spans, as, if not adopted, the
+result will be a canting of the columns from side to side--a very small
+amount, it is true, but sufficient to throw the load upon the extreme
+edges of the base, though the knuckle alone will relieve the top of this
+danger. The author at one time took the trouble to examine, so far as it
+could be done superficially and without opening out the ground to make a
+complete inspection possible, a number of bridges crossing streets, in
+which girders rested upon and were secured to cast-iron columns standing
+in the line of kerb; and he found cracks, either at the top or bottom,
+in about one of every four columns.
+
+When girders passing over columns are not continuous, it may be
+difficult to find room for a double roller and knuckle arrangement; but
+this inconvenience may be overcome by carrying one girder-end wholly
+across the column-top, and securing the next girder-end to it in a
+manner which a little care and ingenuity will render satisfactory, one
+free bearing then serving to carry the load from both girders.
+
+Though the wisdom of using rollers is apparent in spans exceeding some
+moderate length, say 80 feet--as to which engineers do not seem quite
+decided--and varying with the conditions, it need not be overlooked that
+in some cases masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will yield a small
+amount without injury, and though shorter, if resting upon a bottom not
+absolutely rigid, will rock and give the necessary relief; but it is
+obvious, if the resistance to movement is sufficiently great, and the
+girder cannot slide or roll on its bearings, bedstones will probably
+loosen, as, indeed, frequently happens.
+
+
+
+
+CHAPTER II.
+
+MAIN GIRDERS; PLATE-WEBS.
+
+
+It is seldom that girders of this description--or, indeed, of any
+other--show signs of failure from mere defect of strength in the
+principal parts, even though somewhat highly stressed; and instances
+tending to support this statement will be given in a later chapter. For
+the present, it is proposed to indicate peculiarities of behaviour only,
+generally, but not always, harmless.
+
+Though now less often done, it was at one time common practice to load
+plate-girders on the bottom flange by simply resting floor timbers,
+rails, troughs, or cross-girders upon them. In outside girders one
+result of this is to cause the top flange to take a curve in plan,
+convex towards the road, every time the live load comes upon the floor
+of the bridge, upon the passing of which the flange resumes its figure,
+though still affected by that part of the load which is constant.
+
+A bridge of 47 feet span, carrying two lines of way, having one centre
+and two outside girders, with a floor consisting of old Barlow rails,
+resting upon the bottom flanges, showed the peculiarity named in a
+marked degree.
+
+The outside girders, under dead load only, were, as to the top flanges
+(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of
+straight in their length, but upon the passing of a goods engine and
+train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one
+outside girder, and 2-3/16 inches for the other.
+
+The centre girder, having a broader and heavier top flange, curved 5/8
+inch towards whichever road might be loaded. The effect of such
+horizontal flexure is clearly to induce stresses of tension and
+compression in the flanges, which, being (for the top flange) compounded
+with the normal compressive stress due to load carried, results in a
+considerable want of uniformity across the section.
+
+[Illustration: FIG. 4.]
+
+In the case under notice, the writer estimates the stresses for an outer
+girder top flange at 4·5 tons per square inch compression for simple
+loading, and 5·5 tons per square inch of tension and compression, on the
+inner and outer edges, due to flexure, resulting when compounded in a
+stress of 1 ton per square inch tension on the inside, and 10 tons per
+square inch compression on the outside edge. In this rather extreme case
+the stress on the inner edge, or that nearest the load, is reversed in
+character.
+
+The effect described appears to be not wholly due to the twisting
+moment. It is apparent that whatever curvature may be induced by
+twisting alone must be aggravated in the compression flange by its being
+put out of line.
+
+The writer does not attempt here to apportion the two effects in any
+other way than to say that the greater part of the flexure appears to be
+due to the secondary cause. Consistent with this view of the matter is
+the fact that the inclination of the girder towards the rails greatly
+exceeded the calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the floor rails
+bore hard at their extreme ends, at which point of bearing the
+calculated twisting moment accounts for less than one-half of the
+flexure observed in the flanges.
+
+[Illustration: FIG. 5.]
+
+The girders upon removal in the course of reconstruction again took the
+straight form, showing that the very frequent development of the
+stresses named had not sensibly injured the metal, though the bridge
+carried as many as three hundred trains daily in each direction, and had
+done so for very many years.
+
+The deformation of the top flange only has been noticed, yet the same
+tendency exists in the bottom, though the actual amount is much less,
+both because the lower flanges are in tension, and are also in great
+degree confined by the frictional contact of the cross bearers, even
+where no proper ties are used. In the case dealt with the bottom flanges
+of the outer girders curved 1/8 inch outwards only.
+
+With the broad flanges commonly adopted in English practice, twisting of
+the girders, under conditions similar to the above, will not generally
+be a serious matter; but with narrow flanges possessing little lateral
+stiffness it might be a source of danger.
+
+[Illustration: FIG. 6. FIG. 7.]
+
+The twisting may be limited in amount by introducing a cross-frame
+between the girders, from which they are stiffened; by strutting the
+girders immediately from the floor itself, in which case they cannot
+cant to a greater extent than that which corresponds to the floor
+deflection; or by designing the top flange to be unsymmetrical with
+reference to the web, as in Figs. 6 and 7, with the object of insuring
+that under the joint effect of vertical loading and twisting, the stress
+in the flange shall at maximum loads be uniform across the section, and
+allow it to remain straight. This may be secured by making the
+eccentricity of the flange section equal to that of the loading. For
+instance, if the load be applied 3 inches away from the web centre, the
+flange should have its centre of gravity 3 inches on the other side of
+the centre line. It can be shown that this is true throughout the length
+of the girder, and irrespective of the depth. An instance in which
+flange eccentricity being in excess, curvature outwards resulted, will
+be found in a later chapter on deformations, etc. It will not generally
+be necessary to make the bottom flange eccentric, as it is commonly tied
+in some way; but if done, the eccentricity should be on the same side as
+for the top. The flanges remaining straight under these conditions are
+not subject to the complications of stress referred to in the case first
+quoted. The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the kind
+discussed.
+
+It should be remarked that by the two first methods, if the stiffening
+frames are wide apart and attached direct to the web, there is a
+liability for this to tear, under distress, rather than keep the girder
+in line.
+
+There is one other possible consequence of throwing load upon the
+flanges of a girder of a much more alarming nature. In girders not very
+well stiffened, it may happen that the frequent application of load in
+this manner finally so injures the web-plate, just above the top edge of
+the bottom angle-bars, as to cause it to rip in a horizontal direction.
+More likely is this to happen with a centre girder taking load first on
+one side, then on the other, and again on both together. Cases may be
+cited in which cracks right through the webs 3 feet or more in length
+have resulted from this cause. It is very probable, however, that in
+some of these cases the matter was aggravated by the use of a poor iron
+in the webs, as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a girder, would,
+if they could not be made thin enough, even encourage the use of an
+indifferent metal as being quite good enough for that part of the work.
+
+An instance of web-fracture from somewhat similar causes may be here
+given.
+
+In a bridge of 31 feet 6 inches effective span, and consisting of twin
+girders carrying rails between, as shown in Figs. 8 and 9, the load
+resting upon the inner ledges, formed by the bottom flange, induced
+such a bending and tearing action along the web just above the
+angle-bars, as to cause a rip in one of the girders, well open for some
+distance, and which could be traced for 14 feet as a continuous crack.
+
+[Illustration: FIG. 8.]
+
+[Illustration: FIG. 9.]
+
+It will be noticed in the figure that the [T] stiffeners occur only at
+the outer face of the web, and that the inner vertical strips stop short
+at the top edge of the angles, the result being that under load the
+flange would tend to twist around some point, say A, at each stiffener,
+inducing a serious stress in the thin web at that place, while away from
+these stiffeners the web would be more free to yield without tearing.
+The fact that at a number of the stiffeners incipient cracks were
+observed, some only a few inches long, suggests this view of the matter.
+
+A case of web-failure from other influences coming under notice showed
+breaks at the upper part of the web extending downwards.
+
+In this bridge, of 32 feet span, which had been in existence thirty-two
+years, the webs--originally 1/4 inch thick--were, largely because of
+cinder ballast in contact with them, so badly wasted as to be generally
+little thicker than a crown-piece, and in places were eaten through; in
+addition to which, the road being on a sharp curve, the rail-balks had
+been strutted from the webs to keep them in position, the effect of
+which would be to exert a hammering thrust upon the face of the web at
+the abutting ends, and assist in starting cracks in webs already much
+corroded. A feature of this case, tending to show that the breaks
+resulted as the joint effect of waste and ill-usage by the strut
+members, rather than by excessive stress in the web as reduced, is to be
+found in the fact that the girders when removed were observed to be in
+remarkably good shape--i.e. the camber, marked on the original drawings
+to be 1-1/2 inch, still showed as a perfectly even curve of that rise,
+which would hardly have been the case if the lower flange had been let
+down by web-rupture, the result of excessive web-stresses.
+
+Occasionally webs will crack through the solid unwasted plate, in a line
+nearly vertical; not where shear stress is greatest, but generally at
+some other place, and from no apparent cause, either of stress or
+ill-usage. The writer has observed this only in the case of small
+girders not exceeding 2 feet in depth; and, for want of any better
+reason, attributes these cracks to poor material, coupled with some
+latent defect. In a bridge having some thirty cross-girders, each 26
+feet long, about every other one had a web cracked in this manner after
+many years’ use.
+
+Web-cracks of the kind first indicated, are perhaps, the most probable
+source of danger in plate-girders, of any which are likely to occur. The
+fault is insidious, difficult to detect when first developed, and
+perhaps not seen at all till the bridge, condemned for some other
+reason, has the girders freely exposed and brought into broad light. The
+manner in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of these defects
+an uncertain matter, unless sufficient trouble is occasionally taken to
+render inspection complete.
+
+The manner in which girders with wasted and fractured webs will still
+hang together under heavy loading seems to warrant the deduction that,
+in designing new work, it can hardly be necessary to provide such a
+considerable amount of web-stiffening as is sometimes seen; experience
+showing that defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form of
+cracks.
+
+A case of web-buckling lies, so far, without the author’s experience.
+There is no need to introduce, for web-stresses alone, more stiffening
+than that which corresponds to making the stiffeners do duty as vertical
+struts in an openwork girder; in which case it is sufficient to insure
+that the stiffeners occurring in a length equal to the girder’s depth
+shall, as struts, be strong enough in the aggregate to take the whole
+shear force at the section considered, in no case exceeding this amount
+on one stiffener. For thin webs in which the free breadth is greater
+than one hundred and twenty times the thickness, the diagonal
+compressive stress may be completely ignored, and the thickness
+determined with reference to the diagonal tension stress only.
+
+There is one fault which frequently shows itself in stiffeners though
+not the result of web-stresses, and when performing an additional
+function--viz., the breaking of [T] stiffener knees at the weld, where
+brought down on to the tops of cross-girders, due to the deflection of
+the floor, as shown in Fig. 10. When such knees are used, the angle may
+properly be filled in with a gusset-plate to relieve the weld of strain
+and prevent fracture.
+
+[Illustration: FIG. 10.]
+
+There is some little temptation in practice to make use of the solid web
+as a convenient stop for ballast, or road material. Special means,
+perhaps at the cost of some little trouble, should be adopted, where
+necessary, to avoid this.
+
+
+MAIN GIRDERS; OPEN WEBS.
+
+With these, as with plate-girders, deficiency of strength--i.e. of
+section strength--is seldom so marked as to be a reasonable cause of
+anxiety. In particular instances faults in design may result in stresses
+of an abnormal amount, though rarely to an extent occasioning any ill
+effects. The practice of loading the bottom flanges at a distance from
+the centre, the bad effects of which have already been dealt with as
+applied to plate-girders, is not commonly resorted to in girders having
+open webs, nor are these so liable to be heaped with ballast in
+immediate proximity to essential members of the structure.
+
+Some defects are, however, occasionally seen which may be remarked. Top
+booms of an inverted [U] section are sometimes made with side webs too
+thin, and having the lower edges stiffened insufficiently, or not at
+all. Where this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to sustain the
+compressive stress to which the rest of the boom is liable. The practice
+of putting the greater part of the boom section in an outer flange,
+characteristic of this defect, has the further disadvantage of throwing
+the centre of gravity of the section so near its outer edge as to make
+impracticable the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section is thrown into
+the flange-plates, the centre of gravity of the section has no constant
+position along the boom--an additional inconvenience where correct
+design is aimed at.
+
+These considerations indicate the propriety of arranging the bulk, or
+all, of the section at the sides, thus reducing or getting rid of the
+objections named.
+
+Where the bottom boom consists of side plates, only one point demands
+attention. It is found that, though nominally in tension, the end bays
+are liable occasionally to buckle, as though under compressive stress,
+and need stiffening, not excepting girders which at one end are mounted
+on rollers. This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes, such as
+wind forces, or as in the case of a bridge carrying a railway, in which
+the rigidity of the permanent-way may be such that the bridge-structure,
+in extending towards the roller end, cannot move it sufficiently,
+causing a reversal of stress on the lighter portions of the bottom boom
+at the knuckle end; or by the exposed girder booms becoming very
+sensibly hotter than the bridge floor, and by expanding at a greater
+rate, cause this effect, from which rollers cannot protect them.
+
+In counterbracing consisting of flat bars it is desirable either to
+secure these where they cross other members, or stiffen them in some
+manner to avoid the disagreeable chattering which will otherwise
+commonly be found to occur on the passage of the live load.
+
+Occasionally diagonal ties are made up of two flat bars placed face to
+face, to escape the use of one very thick member. Where this is done,
+the two thicknesses, if not riveted together along the edges, will be
+liable to open, as the result of rusting between the bars in contact,
+when the evil will be aggravated by the greater freedom with which
+moisture will enter the space.
+
+Other matters relating to open-web girders will be more conveniently
+dealt with under their separate headings, particularly a further
+consideration of the relationship subsisting between the booms and floor
+structure.
+
+
+
+
+CHAPTER III.
+
+BRIDGE FLOORS.
+
+
+The floors of bridges commonly give more trouble in maintenance, and
+their defects are more frequently the cause which renders reconstruction
+necessary, apart from reasons not concerning strength, than any other
+part of such structures. When it is considered that this portion of a
+bridge is first affected by impact of the load which comes upon it, and
+is usually light in comparison with the main girders further removed
+from the load, and to which the latter is transferred through the more
+or less elastic floor, the fact will be readily appreciated by those not
+already familiar with it.
+
+The end attachments of cross and longitudinal girders are very liable to
+suffer by loosening of rivets, or, more rarely, by breaking of the
+angle-irons which commonly make such a connection. A not unusual defect
+of old work, which may also sometimes be seen in work quite new, where
+the cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends. There is
+small chance of these ever being properly tight, if the act of riveting
+is rendered difficult by bad design. This is the more objectionable if
+it happens that cross-girder ends abut against opposite sides of the web
+of an intermediate main girder, and are secured by the same rivets
+passing through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which they become
+subject, as the cross-girders take their load and deflect under it,
+will be very apt to loosen them. The author has seen a case of this kind
+(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the
+whole of the cross-girder end rivets were loose, some nearly worn
+through, thus allowing the cross-girders to be carried, not by their
+attachments, but by resting upon the main-girder flanges, which in turn,
+by repeated twisting, tore the web for a length of 4 feet; there was
+also pronounced side flexure of the top booms. The movements generally
+on this bridge (of 42-feet span), whether of main or cross-girders, were
+very considerable and disturbing. It was removed after about
+twenty-three years’ use.
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+There is no necessity, as a rule, for the ends of cross-girders attached
+to the same main girder at opposite sides to be placed in line. The
+author prefers to arrange them to miss, by which device each connection
+is entirely separate, the riveting can be more efficiently executed,
+erection is simplified, and the rivets will be more likely to keep
+tight. Other special cases of cross-girder ends will be dealt with under
+the head “Riveted Connections.”
+
+It is sometimes contended that cross-girders attached at their ends by a
+riveted connection should be designed as for fixed ends, in which case
+they are usually made of the same flange section throughout, with a view
+to satisfy the supposed requirements. But a girder to be rightly
+considered as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction, and no
+overhead bracing, this is so far from being the case as to leave little
+occasion for taking the precaution named. As the cross-girders deflect,
+the main girders will commonly yield slightly, inclining bodily towards
+the cross-girders, if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in this manner is
+usually less than that which corresponds to fixing the cross-girder
+ends, and is, generally, slight. It is, of course, necessary that this
+measure of resistance at the connection should be borne in mind for the
+sake of the joint itself, quite apart from any question of fixing.
+
+Possibly, in quite exceptional cases, where very stiff main girders are
+braced in such a manner as to prevent canting, it may be proper to
+consider the cross-girder ends as fixed, or for those near the bearings
+of heavy main girders; but the author has not met with any example where
+cross-girders, apart from attachments, appear to have suffered from
+neglect of this consideration.
+
+With cross-girders placed on either side of a main girder, and in line,
+it may also, for new work, be desirable to regard the ends as fixed, and
+to detail them with this in view. It does not, however, appear wise to
+carry this assumption to its logical issue, and reduce the flange
+section to any appreciable extent on this account. The fixity of the
+ends will, in any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a moderate effect in
+reducing flange stress at the middle of the loaded floor beam.
+
+[Illustration: FIG. 13. FIG. 14. FIG. 15.]
+
+Similar reasons affect the design of longitudinal girder attachments to
+cross-girders, which, if intended to support rails, cannot of necessity
+be schemed to come other than in line. Where the floor is plated as one
+plane surface, there will not usually be any trouble resulting if no
+special precautions are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving the
+joints of abnormal stress. If the plating is, however, designed in a
+manner which does not present this advantage, or if the floor be of
+timber, it is better to decide whether the connections shall be
+considered as fixed, and made so; or avowedly flexible, and detailed in
+such a manner as to possess a capacity for yielding slightly without
+injury. Those connections are most likely to suffer which are neither of
+the one character nor the other, offering resistance without the ability
+to maintain it. Figs. 13, 14, and 15 give representations of three
+“spring joint” methods of insuring yield in a greater or less degree.
+For small longitudinals it is, perhaps, sufficient to use end angles
+with very broad flanges against the cross-girder web; these to be
+riveted in the manner indicated in Fig. 15.
+
+Liberal depth to floor beams is distinctly advantageous where it can be
+secured, rendering it easier to design the ends in a suitable manner, by
+giving room near mid-depth of the attachment to get in the necessary
+number of rivets; or where the ends are rigidly attached direct to
+vertical members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with a
+correspondingly reduced cant of the main girders and flexure of the
+vertical member, with smaller consequent secondary stresses. In any case
+deep girders will contribute to stiffness of the floor itself,
+favourable in railway bridges to the maintenance of permanent-way in
+good order.
+
+[Illustration: FIGS. 16, 17, 18.]
+
+A point in connection with skew-bridge floors occasionally overlooked is
+the combined effect of the skew, and main girder camber, in throwing the
+floor structure out of truth, if no regard has been paid to this. The
+result is bad cross-girder or other connections; or, in the case of
+bearers running over the tops of main girders, a necessity for special
+packings to bring all fair (Fig. 17). The author has in such cases,
+where cross-girders are used, set the main girder beds at suitable
+levels, in order that the cross-bearers may all be horizontal (see Figs.
+16 and 18). This may not always be permissible; but, however the
+difficulty may be met, it should be dealt with as part of the design.
+For small angles of skew only may it be neglected.
+
+Rivets attaching cross-girder angles to the web will occasionally
+loosen, probably due in most cases to bad work, together with some
+circumstance of aggravation, as in the case of a bridge floor consisting
+of girders spaced 3 feet 6 inches apart, with short timber bearers
+between, carrying rails. In many girders the top row of rivets, of
+ordinary pitch and size, had loosened, allowing the web, about 1/4 inch
+thick, a movement of 1/8 inch vertically. The rails being very close
+down upon the cross-girder tops, though not intended to touch, had at
+some time probably done so, and by “hammering” produced the result
+described.
+
+Plated floors are often found which are objectionable on account of
+their inability to hold water, arising sometimes from bad work, as often
+from wide spacing of rivets. With rivets arranged to be easily got at,
+and pitched not more than 3 inches apart, a tight floor may be expected;
+but it is still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside of the
+plate, and sufficiently long to deliver direct into gutters, where these
+are necessary. Drain-holes should not be less frequent than one to every
+50 square feet of floor, if flat, and may advantageously be more so.
+Gutters should slope well, and care be taken to insure practicable
+joints and good methods of attachment--a matter too often left to take
+care of itself, with considerable after-annoyance as a result.
+
+The use of asphalt, or asphalt concrete, to render a plated floor
+water-tight is hardly to be relied upon for railway bridges, though no
+doubt effective for those carrying roads. It is extremely difficult to
+insure that it shall stand the jarring and disturbance to which it may
+be subject, and under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying of the floor.
+In bulk, as in troughs, it may be useful, but in thin coverings on
+plates it cannot be depended upon.
+
+Floors having plated tops are sometimes finished over abutments or piers
+in a manner which is not satisfactory, either as regards the carrying of
+loads or accessibility for painting. If the plates are carried on to a
+dwarf wall with the intention that the free margin of the plate shall
+rest upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after the girder work
+is in place, making it difficult to insure that the wall really supports
+the plate, the result being that this may have to carry itself as best
+it can. In any case, severe corrosion will occur on the underside, and
+the plate rust through much before the rest of the floor; the masonry
+also will usually be disturbed.
+
+It appears preferable to form the end of the floor with a vertical
+skirting-plate having an angle or angles along the lower edge. This may
+come down to a dwarf wall, but preferably not to touch it, the skirting
+being designed to act as a carrying girder. A convenient arrangement is
+shown in Fig. 19, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the skirting
+referred to being carried continuously along the floor edge, and
+attached to each girder-web, the whole of the more important parts being
+open to the painter.
+
+[Illustration: FIG. 19.]
+
+Trough floors consisting of one or other of the forms of pressed or
+rolled section present the objection that it is almost impracticable to
+arrange an efficient connection at the ends, if they abut against main
+girders, and but little connection is, as a rule, attempted, and
+sometimes none. The result is that the load from these troughs is
+delivered in an objectionable manner, and the ends being open or
+imperfectly closed, water and dirt escape on to the flange, or other
+ledge, which supports them. A description of pressed floor which
+promises to overcome this objection, and provide a ready means of
+attachment to the webs of plate-girders, or of booms having vertical
+plate-webs, has within the last few years been introduced. This has the
+ends shaped in such a manner as to close them and provide a flat surface
+of sufficient area for connection by rivets. Each hollow is separately
+drained by holes with nozzles. Whether this type of trough will develop
+faults of its own, due to over-straining of the metal in the act of
+pressing, remains to be seen; but as it appears possible to produce the
+desired form without any material thinning or thickening of the metal,
+the contention that no severe usage accompanies the process appears to
+be reasonable.
+
+That form of troughing in which the top and bottom portions are
+separately formed, and connected by a horizontal seam of rivets at
+mid-depth, is found in use upon railway bridges to be very liable to
+loosening of those rivets near the ends; less surprising, perhaps,
+because the sloping sides are usually thin.
+
+It is a distinctly difficult matter to join two or more lengths of any
+trough flooring having sloping sides, in a workmanlike manner; the fit
+of covers is apt to be imperfect, and some rivets, being difficult of
+access, are likely to be but indifferently tight, so that if the joint
+occurs where it will be more than lightly stressed, trouble will
+probably follow. A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most severe, any
+leakage come directly upon the girder, and remedial measures be more
+difficult to carry out.
+
+Timber floors of the best timber, close jointed, are more durable than
+might be supposed. The disadvantage is a difficulty in ascertaining the
+precise condition of the timber after many years’ use. The author has
+seen timbers, 9 inches by 9 inches, forming in one length a close floor,
+carried by three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces with the
+foot; whilst in another case, with the same arrangement of girders and
+close-timbered floor, the wood, after being in place for thirty-two
+years, was, when taken out, found to be perfectly sound, with the
+exception of a very few bad places of no great extent. In this instance,
+however, it is known that the floor--pitch-pine--was put in by a
+contractor who prided himself upon the quality of the timber that he
+used; the floor being also covered with tar concrete, which had in this
+instance so well performed its office as to keep the timber quite dry on
+the top.
+
+Jack arches between girders make an excellent floor for road bridges,
+though heavy; and for small bridges may be used to carry rails, if the
+girders are designed to be stiff under load. The apprehension that
+brickwork or concrete will separate from the girder-work, or become
+broken up under even moderate vibration, does not seem to be well
+founded, if the deflection is small and the brickwork or concrete good.
+
+The use of corrugated sheeting as a means of rendering the underside of
+a bridge drop dry cannot be too strongly deprecated. If it must be
+adopted, the arrangement should be such as to permit ready removal for
+inspection and painting. It is evident that by boxing up the floor
+structure, rust is favoured, and serious defects may be developed, not
+to be discovered till the sheeting is removed, or something happens.
+
+[Illustration: FIG. 20.]
+
+A case may be instanced in which it was found, on taking down sheeting
+of this description, that the floor girders, previously hidden, were
+badly wasted in the webs. One of these girders had cracked, as shown in
+Fig. 20, and others were in a condition only less bad.
+
+In any floor carrying ballast or macadam, if means are not adopted to
+keep the road material from the structure of the floor, or from the main
+girders, corrosion may be serious in its effects. Cinder ballast is,
+perhaps, the worst in this respect, in its action upon steel or
+ironwork, being distinctly more damaging than any other kind commonly
+used.
+
+Rail-joints upon bridge floors are to be avoided where practicable by
+the use of rails as long as can be obtained; if the bridge is small
+enough, crossing it in one length. At each joint there is likely to be
+hammering and working extremely detrimental to floor members and
+connections; indeed, it may happen that loose rivets will be found in
+the neighbourhood of such joints, and nowhere else on the bridge. Where
+rail-joints cannot be avoided, their position should, if there be any
+choice, be judiciously selected, and the plate-layers taught to close
+the joints and jam the fish-bolts.
+
+[Illustration: FIG. 21.]
+
+As rail-joints upon a bridge may injuriously affect the floor, so also
+will a weak floor be very trying to the rails. A remarkable instance of
+this has come under the writer’s notice, where a bridge (Fig. 21) of
+three 33-feet spans, having outer and centre main girders, with
+cross-girders spaced 3 feet apart, resting upon the girder flanges, but
+not attached, and carrying two roads, had the permanent-way in a very
+bad state. The rails proper, with supplementary angle-plates, rested
+direct upon the cross-girders, which were decidedly light, and the whole
+floor had much “life” in it, the ill-effect of which was shown in
+thirteen breaks in the angle-plates, in each case near their ends,
+generally at holes.
+
+It appears probable that severe stresses may be thrown upon the parts of
+a floor, whether placed at the level of the bottom booms or of the top,
+by changes of length in the booms due to stress. The author has,
+unfortunately, no direct evidence to offer in reference to this, tending
+either for or against the contention. If an unplated floor of cross and
+longitudinal girders of usual arrangement be at the bottom boom of a
+large bridge, as the boom lengthens with the imposition of load upon the
+bridge, all the cross-girders from the centre towards the abutments will
+be curved horizontally, the middle portion being restrained by the
+longitudinals from moving bodily with the ends. Each cross-girder except
+that at the centre, if there be one, will thus present a figure in plan,
+concave towards the abutment to which it is nearest. This will be
+accompanied by stressing of the connections, and a transfer to the
+longitudinals of as much of the tensile stress properly belonging to the
+booms as the stiffness of the cross-girders may communicate.
+
+This in itself will hardly be considerable, and will be the less on
+account of a slight yielding which may be expected at the end
+connections of each longitudinal; but the effect upon the cross-girders
+by horizontal bending will be much marked. If the case be supposed of a
+200-feet span in steel at ordinary loads and stresses, carrying one line
+of way, with cross-girders 20 feet apart, and having no floor-plates, it
+may be ascertained, neglecting for the moment any slight yielding of the
+longitudinal girder connections, that upon the bridge taking its full
+live load there will be the following approximate results: Movement at
+each end of the end cross-girders of 3/10 inch, equivalent to a force of
+7-1/2 tons, tending to bend them horizontally, and a mean stress on the
+outer edges of the girders, 12 inches wide, of 8 tons per square inch
+due to flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge, of
+3/4 ton per square inch. Normal elongation of the longitudinal girder
+bottom flanges, and compression of the top, modifies the figures
+unfavourably as to the cross-girder top flange. Yielding of the
+connections named before has been neglected in arriving at these
+stresses. If they are sufficiently accommodating to give freely, to a
+mean extent, as between the top and bottom of each joint, of 1/29 inch,
+these results will disappear. It is evident, however, that we cannot
+rely upon good work yielding without the existence of considerable
+forces to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.
+
+The most favourable case has been taken; if now it is assumed that the
+floor has continuous plating, the results would seem to be much more
+astonishing. It will appear on this supposition that the boom stresses,
+instead of being taken wholly by the booms, are about equally divided
+between these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which for the end
+cross-girders will approach 40 tons at each connection--considerably
+more than the vertical reaction under normal loads.
+
+Palpably, these conclusions must be greatly modified by the yield of
+longitudinal girder ends, and slip of the floor rivets in transverse
+seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the
+stress at each, as estimated, would be sufficient to induce shear of
+about 6 tons per square inch--more than enough to cause “slip.” After
+making this allowance, it is still evident there must be very serious
+forces at work about the ends of cross-girders under the conditions
+supposed, probably not less than one half the amounts named, as with
+this reduction the floor rivets should not yield, given reasonably good
+work. It is to be observed that the effect of live load only has been
+introduced, on the presumption that the longitudinals and floor-plating
+have not been riveted up till the main girders have been allowed to
+carry the major part of the dead load; but even this cannot always be
+conceded. The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these possible
+effects, either with the object of rendering the communication of these
+forces harmless, or making the floor so that it shall take little or no
+stress from the main booms, by arranging joints across the floor
+specially designed to yield, the ends of longitudinals being schemed
+with the same object. Where there is no plating, the case is, perhaps,
+sufficiently provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these girders
+upon the top of the cross-girders, when stretching of the bottom flanges
+of the rail-bearers under load may be expected, within a little, to keep
+pace with the lengthening of the main booms.
+
+It would appear that light pressed troughs running across the
+longitudinals would, by yielding in every section, also furnish relief,
+as compared with the rigidity of flat plates.
+
+By placing the floor at a level corresponding to the neutral axis of the
+main girders, the communication of stress to the floor may be avoided;
+but it seldom happens that there is so free a choice as to floor height
+relative to the girders. This solution is, therefore, of limited
+application.
+
+It is obvious that somewhat similar effects must obtain to those
+considered in detail, when the floor structure lies at the level of top
+booms, but with forces of compression from the booms to deal with,
+instead of tension.
+
+
+
+
+CHAPTER IV.
+
+BRACING.
+
+
+Bracing, whether to strengthen a structure against wind, to insure the
+relative positions of its parts, or for any other purpose, cannot be
+arranged with too great care and regard to its possible effects. Forces
+may be induced which the connections will not stand, with loose rivets
+as a consequence, and inefficiency of the bracing itself; or, the
+connections holding good, stresses in the main structure may, perhaps,
+be injuriously altered.
+
+To take a not uncommon case, let us suppose a bridge consisting of four
+main girders placed immediately under rails of ordinary gauge, and
+braced in vertical planes only, right across from one outer girder to
+the other. If the roads were loaded always at the same time, nothing
+objectionable would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and deflects, the bracing
+under the six-foot will endeavour to communicate some part of this load
+to the other pair of girders. If the bracing is so designed that some
+correctly calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections, there
+will be no harmful consequences; but if not, the bracings will most
+probably work at the ends; this, indeed, is what frequently happens.
+There is one other effect which will ensue, if the bracing is wholly
+efficient; a certain twisting movement of the bridge will occur, which
+increases the live load upon the outer girder on the loaded side of the
+bridge to the extent of 10 per cent., with a corresponding lifting force
+at the outer girder on the unloaded side. These amounts are not serious,
+but wholly dispose of any advantage it is conceived will be gained by
+causing the otherwise idle girders to act through the medium of the
+bracing. In road bridges of similar arrangement, over which heavy loads
+may pass on any part of the surface, it is clear that the use of bracing
+between girders should not be taken as justifying the assumption that
+the load is distributed over many girders, and correspondingly light
+sections adopted, unless the effect of twisting on the whole bridge is
+also considered, and justifies this view; for, as already stated in the
+case of the railway bridge, the net result may be to increase the girder
+stresses instead of reducing them. Generally, it may be deduced that the
+better plan for railway bridges is to brace the girders in pairs,
+leaving, in the case supposed, no bracing between the two middle
+girders, though there will be no objection to connecting these by simple
+transverse members of no great stiffness, to assist in checking lateral
+vibration. For road bridges of more than five longitudinal girders,
+equally spaced, it may be advantageous to brace right across, the
+twisting effect with this, or a greater, number of girders not, as a
+rule, leading to any increase of load on any girder. Figs. 22 to 25 give
+the distribution of live load, placed as shown, for 3, 4, 5, and 6
+girders.
+
+It is to be observed that these statements do not apply to cases where
+there may be also a complete system of horizontal bracing, the effect of
+which, in conjunction with cross diagonals, may be greatly different,
+with considerable forces set up in the bracing, and a modification of
+girder stresses.
+
+These effects may be so considerable as to call for special attention in
+design where such an arrangement is adopted.
+
+[Illustration: FIG. 22.]
+
+[Illustration: FIG. 24.]
+
+[Illustration: FIG. 23.]
+
+[Illustration: FIG. 25.]
+
+Somewhat similar straining to that first indicated may occur in bracings
+placed between the girders of a bridge much on the skew. If this is, on
+plan, at right angles to the girders, as is commonly and properly the
+case, the ends will evidently be attached to the girders at points on
+their length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts, and the
+bracing will, if at one end attached near a rigid bearing, transfer some
+part of the load from one girder to the other, notwithstanding that
+both girders may be of the same span and equal extraneous loading. It
+would not be difficult to ascertain the amount of load so transferred
+from a consideration of the relative movements if free, and the loads on
+the two girders necessary to render these movements equal, if the
+deflections were simply vertical; but as there will be some twisting and
+yielding of the girders on their seats, the calculation becomes
+involved. If the bracing is placed at about the middle of the girders,
+the effects noted will be greatly reduced; first, because the difference
+of movements near the centre will be less; second, any given difference
+will correspond to a smaller transference of load; and, third, because
+each girder will there be more free to twist than at the ends. It
+therefore appears that bracings between the girders of a skew bridge
+should not be placed near the bearings, though they may be put, with
+much less risk of injury, near the middle.
+
+Cross-girders on a skew bridge are subject to forces somewhat similar to
+those which may affect bracing, rendering it desirable to design their
+attachments in a manner which shall not aggravate the matter, but rather
+reduce the effects of unequal vertical displacement of their ends where
+secured to the main girders.
+
+Crossed flat bars as bracing members are objectionable on account of
+their tendency to rattle, after working loose; but as this effect only
+ensues in bracing which has first become loose (it being assumed that
+the bars in any case are connected where they cross), this objection is
+not itself vital, though greater rigidity is easily obtained by making
+all such members of a stiff section.
+
+Defective bracing between girders, from neglect of the very considerable
+forces it may be called upon to communicate, is very common; the writer
+has seen many such cases, of which one is here illustrated in Fig. 26.
+
+[Illustration: FIG. 26.]
+
+This bridge, of the section shown, and 85 feet span, had very light web
+structure. The bracings, of which there were two sets, were wholly
+inefficient, the end rivets being loose in enlarged holes. Upon the
+passage of a train there was a positive lurching of the girder tops from
+side to side. The integrity of the bridge was really dependent upon
+such stiffness as there was in the girders, and unplated floor.
+
+A common but indifferent method of keeping the top members of main
+girders in line is by the use of overhead girders alone, frequently
+curved to give the requisite clearance over the road. This cannot be
+considered as wholly inefficient, as sometimes maintained, since it is
+evident that the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must take a greater
+force to distort it than would be necessary to cause deformation of a
+corresponding degree, in an open frame formed by the omission of the
+overhead girder; but it is not a method to be recommended, its precise
+utility is difficult to estimate, and, if the cross-girder attachments
+are of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however, not applicable
+to this arrangement alone. All overhead bracing favours this by
+restraining the tendency of the top booms to cant inwards when the floor
+beams are loaded; and though this restraint may be quite harmless, it is
+desirable that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in its character.
+“Sway” bracing, sometimes introduced at right angles to the bridge
+between opposite verticals, tends to emphasise these effects by
+rendering the cross-section of the bridge still stiffer, besides making
+it a matter of difficulty to ascertain how much of the wind forces on
+the top boom is carried to the abutment by the top system of bracing,
+and how much by the floor. The author does not, however, mean to suggest
+that it cannot be used with propriety, but rather that extreme care is
+desirable in considering its ultimate effect on the rest of the
+structure.
+
+For girders of moderate depth there may be on these grounds a distinct
+advantage in abandoning overhead bracing, and securing rigidity of the
+top boom, and adequate resistance to wind forces, by making the
+connection between the cross-girders and the web members sufficiently
+good to insure, as a whole, a stiff [U]-shaped frame; but this, with the
+ordinary type of rocker arrangement under the main girder bearings, will
+not be entirely free from objection, as canting of the girders due to
+floor loading will throw extreme pressure on the inner end of each
+rocker. There appears to be no reason why the cylindrical knuckle should
+not in this case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.
+
+[Illustration: FIG. 27.]
+
+The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom flanges,
+renders very narrow top booms permissible. This is a decided advantage
+where lightness of appearance is aimed at; but it is not unusual to see
+an attempt made in this direction by introducing gusset plates of very
+ample proportions between vertical members of the girders, and the
+projecting ends of flimsy transoms, carried beyond the width of the
+bridge proper, these being of a section wholly out of proportion to the
+brackets they are supposed to secure. Whatever may be the amount of
+strength necessary at the point A, in Fig. 27, there should not be less
+throughout the transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the vertical
+stiffeners is not, as a rule, great. Information to enable this question
+to be dealt with as a matter of calculation is somewhat scanty; but it
+would appear to be sufficient to insure safety that, for an assumed
+small amount of curvature in the compression member, the forces outwards
+corresponding to this curvature, due to thrust, should be resisted by
+verticals and transoms of strength and stiffness sufficient to restrain
+it from any further flexure. It will, of course, be necessary also to
+take care that the compression member is good as a strut between the
+points of restraint. A simple and sufficiently precise method of dealing
+with this question is much needed. In cases where the floor weight rests
+on the flange projection, it is also necessary to give the transom
+additional strength to an extent enabling it to resist the twisting
+effort between any two of these transverse members; further, resistance
+to wind on the girder has to be provided in both transoms and verticals.
+
+It may be hardly necessary to insist that bracing intended to stiffen a
+structure against wind, local crippling, or vibration, should be made
+complete, not stopping short at some point, because it cannot
+conveniently be carried further, as is sometimes done, unless the
+strength of those parts of the structure through which the forces from
+the bracing must be communicated to the abutments is sufficiently great,
+considered with reference to other stresses in those parts which have
+also to be endured.
+
+Bracing stopped short in this way, making only the central part of a
+bridge rigid, may have the effect of increasing the forces to which the
+unstiffened end members would otherwise be liable. Such a structure
+would evidently be much stiffer against wind-gusts than if no bracing
+existed--the resistance to a blow would be increased; but the power to
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater maximum forces than
+if bracing were wholly omitted. The net effect may still be better than
+with no bracing, the point raised being simply that of an increase of
+stress in particular end members.
+
+In the bracing of tall piers, the rising members of which will be
+subject to any considerable stress, if the diagonal members are not
+finally secured when the piers are under their full load, or an initial
+stress of proper amount induced in those members, the effect of loading
+will be to render them slack; so that an appreciable amount of movement
+at the top may occur before it can be limited by the efficient action of
+the bracings. This effect under blasts of wind or continual passage of
+trains may, indeed, be dangerous. Similar considerations apply to the
+top wind bracing of deep girder bridges, influencing also the bottom
+bracing in a contrary manner, which calls for attention in fixing the
+unit stresses for such members.
+
+The bracing of sea-piers is very liable to slacken if made with
+pin-and-eye ends, as is often done for round rods. The detail presents
+advantages in erection, but is not altogether satisfactory in practice.
+Such connections are continually working. In the finest weather, with
+the sea quite smooth but for an almost imperceptible wave movement, the
+lower parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there room for
+surprise when it is considered that these oscillations, occurring at
+about ten to each minute, never wholly cease, and amount in the course
+of one year to over five million in number.
+
+Bracing attached in such a manner that there can be no initial slack, or
+slack due to wear under endless repetitions of small amounts of stress,
+will have a much better chance to keep tight. The advantage presented
+by round rods in offering little surface to the water, is more than
+negatived by inefficiency of the usual attachments for such rods.
+
+The author has observed that bracing of members possessing some
+stiffness, and with good end attachments to ample surfaces, appears to
+stand best in ordinary sea-pier work. For such structures the bracing
+should consist of a few good members, with a solid form of attachment,
+rather than of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very possibly also, in
+the case of sea-pier work, in unskilled hands. If round rods must be
+used, they will stand much better if made of large diameter.
+
+Before leaving the subject of bracing, it may not be out of place to
+refer to wind pressure, as this may so much affect the proportioning of
+the members.
+
+Some years since the author had occasion to examine a number of
+structures with respect to their stability. Of foot-bridges from 60 feet
+to 120 feet long, three or four, when calculated on the basis
+recommended by the Board of Trade as to pressures upon open-work
+structures, worked out at an overturning pressure of from 18 lb. to 22
+lb. per square foot. These bridges had been many years in existence; it
+is, therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them as to the
+whole surface.
+
+[Illustration: FIG. 28.]
+
+Particulars were taken in 1895 of a notice-board, presenting about 12
+square feet of surface, which was blown down in the great storm of March
+24 of that year, at Bilston, in Staffordshire. It was situated at the
+foot of a slight slope, over which the wind came, striking the
+obstruction at right angles. The board was mounted on two oak posts of
+fair quality and condition, which broke near the ground at bolt holes
+(see Fig. 28). The force required to do this, at 9000 lb. modulus of
+rupture--a moderate value--corresponds to 50 lb. per square foot on the
+surface exposed above the break.
+
+In the same neighbourhood, at the same time, considerable damage was
+wrought in overturning chimney stacks, to buildings and roofs; the
+general impression in the locality being that the storm was of
+exceptional, even unprecedented, violence. Bilston, it should be noted,
+lies high.
+
+At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27
+lb. was registered. In another part of the country it is said to have
+been 37 lb. Wind is so capricious in its effects over small areas as to
+render it probable that the maximum pressures have never been recorded;
+but this is a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by themselves
+insufficient to throw much light on the question, may be of use in
+connection with other known examples.
+
+
+
+
+CHAPTER V.
+
+RIVETED CONNECTIONS.
+
+
+Considerable latitude is observable in the practice of engineers in the
+use of rivets. Numberless experiments to determine the resistance of
+riveted connections have from time to time been made, but these are not
+to be considered by themselves as final, when the results of experience
+in actual construction, are available for further enlightenment.
+
+The class of workmanship so largely influences the degree in which
+rivets will maintain their integrity that it is only by the observation
+of a large number of cases, including all degrees of workmanship, that
+any reliable conclusions may be drawn. In this respect laboratory
+experiments have an apparent advantage, as the conditions may be kept
+sensibly the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must in the end
+determine the utility of any inquiry for practical application.
+
+The author has studied the particulars of a number of cases to ascertain
+under what conditions as to stress, having due regard to the effects of
+vibration, rivets will remain tight, or become loose. Every loose rivet
+that may be found cannot, of course, be taken as being due to excessive
+stress; the more frequent cause is indifferent work, evidenced by the
+fact that neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon the
+remainder. When rivets loosen as the direct result of over-stress, it is
+usually by compression of the shank and enlargement of the hole, or by
+stretching of the rivet and reduction of its diameter. Instances of
+failure by partial or complete shear are extremely rare; indeed, the
+author has never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work, it is not
+uncommon to find it cut or bent as an after consequence.
+
+In estimating stresses at which rivets have remained tight, or loosened,
+as the case may be, examples have generally been chosen in which there
+could be no reasonable doubt as to the amount of those stresses by the
+ordinary methods of computation. This is clearly most important, as, if
+any appreciable uncertainty remained as to the degree of stress, the
+results deduced would be of little value. For this reason those
+instances in which the loads upon girders, or parts of girders, may find
+their way to the supports by more than one route, are to be regarded
+with caution, as are those in which full loading possibly never obtains,
+but which may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been used in
+making the computations; in some cases from direct measurement from
+particular rivets, in others with a suitable allowance for excess
+diameter of hole, according to the class of work under consideration.
+
+Dealing first with main girders, it may be said that rivets attaching
+the webs of plate girders to the flange angles rarely loosen, though
+subject to considerable stress. In illustration of this may be named a
+bridge for two lines of way, 85 feet effective span, having two main
+girders with plate webs, and cross-girders resting on the top flanges,
+previously referred to (see Fig. 26).
+
+The girders, which were 6 feet 9 inches deep, had a bearing upon the
+abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches
+pitch. There is in a case of this kind some little uncertainty as to
+what is the stress on the flange angle rivets at, or very near to, the
+bearings; but, taking the vertical rows of rivets at the web joints near
+the ends as presenting less uncertainty, the stress per rivet works out
+at 4·8 tons, being 4 tons per square inch on each shear surface, and 11
+tons per square inch bearing pressure upon the shank in the web plate,
+which was barely 1/2 inch thick. This bridge was frequently loaded upon
+both roads, but with one road only carrying live load, the stresses in
+the more heavily loaded girder would be fully 90 per cent. of those
+obtaining as a maximum. There was on this bridge, which had been in use
+31 years, considerable movement and vibration.
+
+It is by no means uncommon to find cases of rivets in main girders
+taking 11 tons per square inch bearing pressure--occasionally more--and
+remaining tight. As furnishing an instructive, though slightly
+ambiguous, instance of rivets in single shear, may be cited a bridge not
+greatly less than that just referred to, of about 65 feet span, carrying
+two lines of way, there being two outer and one centre main girder of
+multiple lattice type, with cross-girders in one length 4 feet apart,
+riveted to the bottom booms of the main girders; these rivets, by the
+way, were in tension. The floor was plated, the road consisting of stout
+timber longitudinals, chairs, and rails (Fig. 29).
+
+[Illustration: FIG. 29.]
+
+It should be noted that there is in this case some difficulty in
+ascertaining the precise behaviour of the cross-girders, affecting the
+proportion of load carried by the outer and the inner main girders.
+Strict continuity of all the cross-girders could only obtain if the
+deflection of the main girders were such as to keep the three points of
+suspension of each cross-girder in the same straight line. A close
+inquiry showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would, under load,
+by relative depression of the middle point of support, be reduced to
+the condition of two simple beams, those at the extreme ends of the span
+would behave as continuous girders.
+
+With both roads carrying engine loads equal to those coming upon the
+bridge, the author estimates that for the centre main girder the shear
+on the rivets of the end diagonals, secured by one rivet only, was 14·9
+tons per square inch, and the bearing pressure 16·3 tons; the flange
+stress being 7·1 tons per square inch net. The outer main girders are
+most heavily stressed when but one road, next to the outer girder
+considered, carries live load. For this condition the stresses work out
+at 9 tons per square inch shear on the rivets of the end diagonals, and
+9 tons bearing pressure, the flange stress being 5·7 tons per square
+inch on the net section.
+
+Without intending to throw any doubt upon the substantial truth of these
+results, it must be admitted that instances of greater simplicity of
+stress determination are much to be preferred. For purposes of
+comparison, but not as having any other value, the results have also
+been worked out on the supposition of all cross-girders acting each as
+two simple beams, and also for strict continuity, and are here
+tabulated, together with the conclusions given above.
+
+The cross-girders were moderately stressed, and the tension on the
+rivets attaching them to the main girders probably did not exceed 3 tons
+per square inch.
+
+It should be pointed out that the traffic over the bridge was small. The
+centre main girder but seldom bore its full load, though at all times
+liable to receive it. Much importance cannot, therefore, be attached to
+the results for this girder, other than as showing how a structure may
+stand for many years, though liable at any time to the development of
+stresses which would commonly be regarded as destructive, or nearly so.
+
+EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS.
+
+  ---------------------------------+-----------+------------+---------
+                                   |   Cross-  |   Cross-   |
+                                   |  Girders  | Girders as | Correct
+                                   | as Simple | Continuous | Results.
+                  --               |   Beams.  |   Beams.   |
+                                   +-----------+------------+---------
+                                   | Stress in Tons per Square Inch.
+  ---------------------------------+-----------+------------+---------
+  Centre girder, 63 ft. span (both |           |            |
+  roads loaded):                   |           |            |
+    Rivets in diagonals--Shear     |    13·7   |    17·2    |  14·9
+          Do.            Bearing   |           |            |
+                         pressure  |    15·0   |    18·8    |  16·3
+                         Flange    |           |            |
+                         stress    |     6·8   |     8·5    |   7·1
+                                   |           |            |
+  Outer girder, 66 ft. span (near  |           |            |
+  road loaded):                    |           |            |
+    Rivets in diagonals--Shear     |     9·6   |     8·2    |   9·0
+          Do.            Bearing   |           |            |
+                         pressure  |     9·6   |     8·2    |   9·0
+                         Flange    |           |            |
+                         stress    |     5·9   |     5·1    |   5·7
+  ---------------------------------+-----------+------------+---------
+
+The material and workmanship of the bridge were good. The rivets of the
+centre girder end diagonals, 1 inch in diameter, were originally 7/8
+inch, but on becoming loose were cut out, the holes reamered, and
+replaced by the larger size, which remained tight, and to which the
+stress figures apply. The rivets in the diagonals near the centre, 7/8
+inch in diameter, which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The riveting in the
+outer girder diagonals, subject to smaller stresses, much more
+frequently developed, also gave trouble, particularly those liable to
+counter stresses.
+
+Apart from looseness of rivets, the general appearance and behaviour of
+the bridge, which had been in existence about twenty years, was not
+suggestive of any weakness.
+
+Of smaller girders, an example showing the necessity for care in
+discriminating, if it be possible, between looseness of rivets resulting
+from over-stress and that due to other influences may first be quoted.
+Two trough girders, of 11 feet effective span, each of the section shown
+in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle,
+with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch
+pitch, showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (Fig. 31). From the nature of the
+arrangement the lower web rivets, which were loose, would receive the
+first shock of the load coming upon the span, but there were evidences
+indicative of original bad work. The angle bars gaped, suggesting that
+these had first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets failing to
+pull the work close, and then readily working loose. Here there is
+considerable uncertainty as to how much of the loosening is to be
+attributed to bad work, and how much to stress. It may, however, be
+remarked that whatever bearing stress was the ultimate result of the
+load hammering on the lower angle flanges, loosening rivets never
+perhaps really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable
+impactive force, was not sufficient to loosen these. The girders were
+taken out after being in place sixteen years.
+
+[Illustration: FIG. 32.]
+
+[Illustration: FIG. 30.]
+
+[Illustration: FIG. 31.]
+
+An instance of undoubted excessive bearing pressure was found in the
+cross-girders of a bridge, mentioned on p. 15, of which so many web
+plates were cracked. This bridge, carrying two lines of way, had outer
+main girders, and long cross-girders with 1/4-inch webs and 3/4-inch
+rivets, 4 inches pitch. The rivet stresses work out at 4·3 tons per
+square inch on each shear surface, and 24 tons per square inch bearing
+pressure. For one road only being loaded, the latter figure falls to
+18·5 tons. The traffic over this bridge, twenty years old, was
+considerable, rapid, and heavy. It is hardly necessary to add that a
+large number of the rivets were loose, one of which is shown in Fig. 32.
+
+[Illustration: FIG. 33.]
+
+To take another case relating to a floor system of extremely bad design
+(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor
+having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches
+deep, supporting hog-backed trough longitudinals. The cross-girders were
+at their ends but 6-3/4 inches deep, the distance from the bearing of
+cross-girders to centre of longitudinals carrying a rail being 2 feet 10
+inches, in which length were eight rivets in the web and angles at the
+top, and six at the bottom, all 3/4 inch in diameter.
+
+The shear stress on the upper rivets works out at 7·3 tons per square
+inch on each shear surface, the bearing pressure 20·6 tons per square
+inch. On the lower rivets the shear stress becomes 9·7 tons, and the
+bearing pressure 27·4 tons, per square inch. Care was exercised in
+computing these stresses, that part of the bending moment carried by the
+web being allowed for, but it must be admitted that the result is,
+probably, approximate only. The sketch here given shows the cross-girder
+end and section. The rivets, though in double shear, were, as might be
+expected, loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled after twelve
+years’ use.
+
+In illustration of the behaviour of rivets in the ends of long
+cross-girders, both shallow and weak, and many years in use under heavy
+traffic, may be cited connections having end angle bars to the
+cross-girders, with six rivets through the web of main girders. The
+bearing pressure worked out at 7·8 tons per square inch. Many rivets
+were loose, but it should be remarked that the workmanship was not of
+the best class, and the cross girders flexible: a characteristic very
+trying to end rivets, and inducing a stretch in some, already referred
+to as a possible cause of loosening. This will be apparent if the
+probable end slope of weak girders be considered. The author concludes
+that this inclination should not, for ordinary cases, exceed 1 in 250;
+but the ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly regarded as bad
+practice to submit rivets to tension, yet this is frequently, though
+unintentionally, permitted in end attachments, without any attempt to
+limit the amount of tension. With suitable restrictions, there appears
+no serious objection to rivet tension for many situations.
+
+Another instance of cross-girder end connections of a different type is
+illustrated in Fig. 34.
+
+The main girders of the bridge were 12 feet apart, each cross-girder end
+carrying its share of the half of one road. The mean bearing pressure
+upon the rivet shanks works out at 5·8 tons per square inch for the six
+rivets of the original joint, but in the particular joint shown some of
+the rivets had loosened, making the bearing pressure upon the remainder
+about 8·7 tons per square inch. It is apparent there must have been
+considerable stress on the top and bottom rivets which loosened. These
+two rivets would also, because of difficult access, be in all likelihood
+insufficiently hammered up. The joints worked rather badly; the loose
+rivets had “cut” to a considerable extent, a process materially assisted
+by the gritty nature of the ballast (limestone), particles of which,
+getting into the joint, contributed to the sawing action; this had
+clearly been taking effect for some considerable time. (See Fig. 35.)
+
+[Illustration: FIG. 34.]
+
+[Illustration: FIG. 35.]
+
+The two cases of cross-girder ends given are both rather exceptional in
+character, and in each case the defects appear to be due to general bad
+design and workmanship rather than to any serious excess of bearing
+pressure. This may be illustrated by taking the common case of
+cross-girders, 2 feet deep, carrying two roads, and having end angle
+irons riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which is, for old
+work, simply typical, and does not relate to any specific instance, the
+bearing pressure on the rivets will work out at from 6 to 8 tons per
+square inch, and will seldom be accompanied by looseness of rivets, and
+then only as a result of faulty work.
+
+Some sketches of rivets taken from old bridges have already been given
+in connection with the cases to which they belong; a few others are here
+shown (Figs. 36 to 40) to further illustrate what may be the actual
+condition of rivets after some years’ use, and how different from the
+ideal rivet upon which calculations are based. These are, however, bad
+instances.
+
+[Illustration: FIG. 36.]
+
+[Illustration: FIG. 37.]
+
+[Illustration: FIG. 38.]
+
+[Illustration: FIG. 39.]
+
+[Illustration: FIG. 40.]
+
+It should be noticed that rivets may, if in double shear, be loose in
+the middle thickness, due to enlargement of the hole in the central part
+and compression of the rivet, and yet show no sign of this by testing
+with the hammer. There is, however, generally marked evidence of another
+kind in the “working” of the inner part, as, for instance, the web of a
+plate girder, in which case a discoloration due to rust is to be found
+along the edges of the angle bars, or a movement may be detected on the
+passage of live load. Red rust is, in fact, frequently an indication of
+something wrong, when no other evidence is apparent. In plate girders
+having [T] or [L] bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching these
+bars to the cross-girder tops loose, due to causes already dealt with.
+The riveted connection should, as to strength, bear some relation to the
+strength and stiffness of the parts secured, if the rivets are to remain
+sound.
+
+It may be well to give here a summarised statement of the results
+already named, for purposes of ready reference. These by themselves are
+not sufficient to enable working stresses to be deduced, though they are
+instructive. The author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which the rivets
+behaved well, but is not now able to give precise particulars of these.
+
+EXAMPLES OF RIVET STRESSES.
+
+  ---------+-----+---------+------+------+--------+-----------------
+     --    |Span |  Where  |Shear |Single|Bearing | Tight or Loose.
+           | in  |  Found. |Stress|  or  |Pressure|
+           |Feet.|         |  in  |Double|in Tons |
+           |     |         | Tons |Shear.|  per   |
+           |     |         |  per |      | Square |
+           |     |         |Square|      | Inch.  |
+           |     |         |Inch. |      |        |
+  ---------+-----+---------+------+------+--------+-----------------
+  Main    {|  85 |   Web   |  4·0 |   D  |  11·0  | Tight.
+  girders {|  66 |Diagonals|  9·0 |   S  |   9·0  | Many loose.
+          {|  63 |    „    | 14·9 |   S  |  16·3  | Tight generally.
+           |     |         |      |      |        |
+          {|  11 |   Web   |  1·4 |   D  |   7·0  | Tight.
+  Small   {|  26 |    „    |  4·3 |   D  |  24·0  | Many loose.
+  girders {|  11 |    „    |  7·3 |   D  |  20·6  | Loose.
+          {|  11 |    „    |  9·7 |   D  |  27·4  | Loose.
+           |     |         |      |      |        |
+  End     {|  27 |   Ends  |  5·4 |   S  |   7·8  | Loose.
+  connec- {|  12 |    „    |  1·8 |   D  |  {5·8  |}Many loose.
+  tions   {|     |         |      |      |  {8·7  |}
+           |     |         |      |      |        |
+  (Type    |     |         |      |      |        |
+  case)    |  26 |    „    |  4·8 |   S  |   7·0  | Tight.
+  ---------+-----+---------+------+------+--------+-----------------
+
+It is probable that the fact of a rivet being in single or in double
+shear largely affects its ability to resist the effects of bearing
+pressure, as commonly estimated. In the first case, the rivet-shank must
+bear heavily on the half-thickness of the plates or bars through which
+it passes, rather than on the whole thickness; and it is to be supposed
+that under this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.
+
+[Illustration: FIG. 41.]
+
+[Illustration: FIG. 42.]
+
+The author has no very definite information in support of this
+contention, but suggests that for double shear the permissible bearing
+pressure may probably be as much as 50 per cent. greater than for rivets
+in single shear; the difference being made rather in the direction of
+increasing the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this is evident when
+it is considered that the practice has commonly been to make no
+distinction, so that whatever bearing pressures are found to be
+sufficient for both cases may be increased for those capable of taking
+the greater amount. Figs. 41 and 42, here given, illustrate the
+behaviour of rivets under the two conditions.
+
+With reference to the amounts of the stresses to which rivets may be
+subject, the author concludes, as a result of his experience, coupled
+with a consideration of known laboratory tests, that for all dead load
+these may be quite prudently higher than is frequently taken. For iron
+the shear stress to be 10 per cent. less than the stress of parts
+joined; and the bearing pressure--for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary mild
+steel the shear stress to be 20 per cent. less than the stress in parts
+connected, and the bearing pressure equal to it for single-shear rivets;
+and 50 per cent. more for rivets in double shear, though the two latter
+values may probably approach those for wrought iron in steel of the
+higher grades sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction of the
+nominal working stress, arrived at by any one of the methods in use
+which may be adopted, affecting both the parts connected, and the rivets
+connecting them. For reverse stresses it is advisable to keep the shear
+stress in any rivet so low, say 3 tons per square inch, that the
+frictional resistance of the parts gripped by the rivets shall be
+sufficient to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure that,
+if brought to a bearing in one direction by the greater force, it shall
+not go back with reversal of stress. This requirement may be open to
+some question with respect to good machine-riveted work, but for
+hand-riveted connections it may certainly be adopted with wisdom.
+
+The following table will show at a glance how the stresses proposed vary
+with the unit stresses governing the main sections.
+
+PROPOSED TABLE OF RIVET STRESSES.
+
+  -----------+-------------+----------------+----------------
+  Unit Stress|             |Bearing Pressure|Bearing Pressure
+      in     |Shear Stress.|for Single-Shear|for Double-Shear
+    Member.  |             |     Rivets.    |    Rivets.
+  -----------+-------------+----------------+----------------
+              _Wrought Iron.--Tons per Square Inch._
+       3·0   |     2·7     |       3·6      |       5·4
+       4·0   |     3·6     |       4·8      |       7·2
+       5·0   |     4·5     |       6·0      |       9·0
+       6·0   |     5·4     |       7·2      |      10·8
+       7·0   |     6·3     |       8·4      |      12·6
+                 _Steel.--Tons per Square Inch._
+       4·0   |     3·2     |       4·0      |       6·0
+       5·0   |     4·0     |       5·0      |       7·5
+       6·0   |     4·8     |       6·0      |       9·0
+       7·0   |     5·6     |       7·0      |      10·5
+       8·0   |     6·4     |       8·0      |      12·0
+       9·0   |     7·2     |       9·0      |      13·5
+  -----------+-------------+----------------+----------------
+
+  NOTE.--Tension on rivets to be limited to one-half the permissible
+  shear stress, the holes being slightly countersunk under snap-head.
+
+It may be objected that the shear stresses in the proposed table are
+somewhat high for wrought iron and steel. This feature is intentional,
+and is supported by the consideration that whereas there may be loss of
+strength in the members of a structure by waste, there is no such loss
+in rivets, if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective field rivets
+is left to be dealt with as may be considered advisable for each
+particular case, the table as it stands being applicable only to
+riveting not below the standard of first-rate hand work.
+
+Cases of loose rivets in main girders over 50 feet span, due to any
+cause but bad work, are extremely rare, unless resulting from the action
+of some other part of the structure. It may be stated broadly that for
+railway bridges of less than perfect design, the nearer the rail, the
+more loose rivets, generally at connections. This is, no doubt, largely
+due to the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead load, and
+because this effect has been but little modified by the elasticity of
+any considerable length of intervening girder-work. In addition to this,
+it is quite usual to find the rivets more heavily stressed, even though
+the load be considered as “static,” in the floor system than in the
+main-girders, though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting--viz., the
+connections--are commonly dealt with by hand; and for this reason it is
+the more necessary to design these with the greatest care.
+
+Any arrangement which favours the gradual acceptance of stress by one
+part from another will contribute to the integrity of riveted
+connections, and lessen the liability of the material to develop faults.
+In other branches of design this is well recognised, but appears in much
+old bridge work to have been entirely overlooked.
+
+Bridges carrying public roads very seldom furnish examples of loose
+rivets; the conditions are generally much more favourable, impact being
+practically absent, full loading infrequent, and the proportion of dead
+load to live, high.
+
+It is, perhaps, hardly necessary to insist upon rivets being, apart from
+mere considerations of strength, sufficiently near together to insure
+close work and exclude moisture. Outside edge seams should never be more
+widely spaced than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections, the
+greater stiffness of the section makes wider spacing allowable up to,
+say, 20 times the thickness; but this must be governed largely by the
+amount of riveting required to pull the parts close together. Where more
+than four thicknesses are to be gripped by the rivets, 3/4 inch in
+diameter is hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed 5/8 inch thick.
+
+
+
+
+CHAPTER VI.
+
+HIGH STRESS.
+
+
+High stress, provided it be well below that at which immediate injury
+results, or possible failure, is not uniformly objectionable. It may be
+first considered relative to the absolute and elastic limits of
+strength, next with respect to the range of stress, and, finally, with
+regard to the frequency of application. For practical purposes--that is,
+for the continued efficiency of a structure--the limit of elasticity
+must be considered to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long as it
+lasts, be liable to the original measure of stress. There may be places
+in a bridge, however, over-stressed only in the earlier period of its
+existence, which, by being over-stressed and suffering deformation,
+permit the origin of this distortion to be harmlessly met in some other
+way. In such a case the injury done to that part does not, of necessity,
+lead to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail after
+being in use but a short time. As for riveting, so in dealing with the
+amount of stress to which a member is supposed to be liable, it should
+be clearly understood by what method this has been arrived at, whether
+the value assigned is the actual measure of the stress, or simply the
+conventional amount arrived at in the conventional way; perhaps
+neglecting web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal amount of
+stress, or including only a partial recognition of those influences. In
+any case quoted the stress named is that at which the author arrives by
+the ordinary methods of computation carefully applied, where these
+appear to be sufficiently precise, unless any qualifying remark be
+added. Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that basis, and
+deducing the stress at the holes from the ratio of net to gross section
+at the extreme fibres; a method more correct than by reference to the
+moment of inertia of the net section. Any exhaustive refinement in the
+study of stresses is not attempted, both because it is beyond the
+author’s powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation in
+practice. Effective spans are taken at moderate values, and all
+exaggeration is avoided.
+
+The effects of impact in any part vary so much with nearness to, or
+remoteness from, the living load, and the frequency of development of
+the maximum stress from all causes acting together is so much affected
+by the same consideration, that it is apparent a nominal stress which
+may be harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as ordinarily
+stated--i.e., at so much per square inch, uniform across a section--is
+seldom a cause of trouble. In nearly all cases of failure there is an
+accompanying localised destructive stress, either in rivets or
+elsewhere, with crippling or deformation of some essential part. In the
+tension flanges of main girders with uncomplicated stress, this may run
+up to an amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the compression
+flanges, if these be in themselves sufficiently stiff, or properly
+restrained from side flexure. In support of the above statement may be
+quoted the following instances relating to wrought-iron structures:--
+
+A bridge of 60 feet effective span, having girders immediately under the
+rails, had a flange stress of 6·3 tons per square inch. Another of 64
+feet span, carrying two lines of way, with outside main girders and
+cross-girders, had the flanges of the former stressed to 6·8 tons per
+square inch. A third, of 76 feet span, of similar construction to the
+last, was stressed in the main girder flanges to 7·5 tons per square
+inch. The webs were not included in the computation; the figures,
+therefore, compare with ordinary practice. In these three cases the main
+girders showed no signs of distress, referable to the results stated,
+though the top flanges in the last case were curved inwards. The effect
+of this flexing of the flange would be, of course, to increase the
+amount of compressive stress along one edge, though to what degree
+cannot now be stated.
+
+[Illustration: FIG. 43.]
+
+[Illustration: FIG. 45.]
+
+[Illustration: FIG. 44.]
+
+A further instance of considerable flange stress occurred in a bridge of
+seven nearly equal continuous spans, 25 feet generally, the end and
+greatest span being 29 feet 6 inches, centre to centre of bearings. Some
+details of the bridge are given in Figs. 43 to 45. The four inner main
+girders under rails were 2 feet deep, with webs 1/2 inch thick over
+piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3
+inches by 3 inches by 5/8 inch. There were also two outer girders of the
+same depth, with single [L] bars. Plate diaphragms of full girder depth
+and particularly stiff were carried right across the bridge at the
+centre of the spans, and over the piers. The girders, though evidently
+designed to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see Fig. 45). It is
+doubtful if the girders acted with strict continuity for long after
+erection, as the excessive stress in the rivets of the flange joint
+would, for that condition, have been nearly sufficient to shear them. It
+is probable that this being so, the joints first yielded, relieving the
+bending moment over the piers, and increasing it near mid-span. Whether
+the end spans be considered as strictly continuous with the rest, or as
+simple beams, the maximum bending moments would not greatly differ,
+though occurring for continuity over the pier, for free beams at the
+centre. There is, however, an intermediate condition which makes the
+moments at these two places less than either maximum, but equal to each
+other; a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been calculated,
+giving the minimum stress value that can be accepted. The diaphragm has
+been assumed to transfer to the outer girders a due proportion of the
+load. With this explanation it may now be stated that, under engine
+loads corresponding to those running, the flange stress worked out at
+7·4 tons per square inch tension, web included, or 9·7 tons per square
+inch without considering the web; which stresses, it is more than
+probable, may have been greater. The figures include the consideration
+of anything which may contribute to lowering the stress, and are hardly
+to be compared with those worked to in ordinary design of new work, in
+which it would be quite usual to neglect the assistance of the outer
+girders and the webs, to work to heaviest engine-loads, and possibly
+include an allowance for the effects of settlement. Dealt with in this
+way the girders would seem to be of about one-fourth the strength that
+would be required in the design of a new bridge, in which certain
+elements of strength would be deliberately ignored.
+
+The ironwork was in good condition, there was no ordinary evidence of
+weakness apart from the calculated results, the vibration was distinctly
+moderate, and the deflection, though not recorded, was certainly small.
+The bridge did, indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long overstressed
+may have a sensibly higher modulus of elasticity than newer work at more
+moderate stresses. The traffic was not very considerable, and both
+roads, of the same spans, but seldom loaded at the same time; though
+with this construction of bridge there would in either case be very
+little difference. The author recalls no reason for supposing that the
+piers had yielded in any sensible degree. The bridge was rebuilt after
+some thirty-six years’ use.
+
+Stress of considerable amount in the flanges of a latticed main girder
+of 63 feet span has already been noticed in the chapter on “Riveted
+Connections,” which for the tension boom worked out to 7·1 tons per
+square inch, the flanges in this case showing no signs of weakness. An
+instance has also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons per square
+inch, the girder recovering its form when relieved of load.
+
+As to stress in cross-girder flanges, an example may be quoted of a
+bridge of 109 feet span, carrying two roads, having outside main
+girders, with cross-girders between; these latter were stressed in the
+flanges to 6·7 tons per square inch (webs not included), if the partial
+distribution among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some reason to
+think in this instance that distribution had the effect of reducing the
+stress quoted, as the observed deflection of the cross-girders was
+materially less than that calculated for girders acting independently of
+each other, though this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the heavy main
+girders, would also tend to moderate the stress. No very definite
+conclusion can therefore be deduced from this instance.
+
+To take another case of less uncertainty, the bridge of 35 feet span
+(see Fig. 33), referred to in “Riveted Connections,” may again be cited.
+The extreme fibre stress in the cross-girder flanges worked out at 6·3
+tons per square inch, web included, or 6·5 tons, exclusive of the web.
+It cannot be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was 1/2 inch on the span of
+11 feet, in addition to a permanent set of 3/4 inch, largely due,
+however, to “working” rivets.
+
+A better and altogether conclusive case of the way in which
+cross-girders may occasionally suffer considerable stress, and show no
+sign, is furnished by two cross-girders, of which some particulars are
+here given. These girders occurred in the floor of a very acute angled
+skew bridge, riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end on a masonry
+abutment. The first girder was about 19 feet effective span, 12 inches
+deep in the web, with angle bar and plate flanges. The girders were
+spaced 6 feet apart, and were connected under the rails by [T]-bars,
+cranked down to face the webs, and riveted through. Though these [T]’s
+had little stiffness, yet the frequent vertical movements of the girders
+relative to each other, under passing loads, had broken the majority of
+the [T]-bars at the bends, so that no notice need be taken of these as
+transferring load from any one cross-girder to its neighbour. The floor
+covering consisted of timbers about 4 inches thick, also incompetent to
+transfer any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers, chairs,
+and ordinary bull-headed rails. The stress to which the girder was
+liable works out at 8·4 tons per square inch, on the extreme fibres of
+the net section, web included; or 9·1 tons, neglecting the web, under
+engine-loads of a common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with angle bar
+and plate flanges. The stress per square inch was 10·5 tons, web
+included, or 11·1 tons per square inch, neglecting the web. This girder
+carried three rails, one of which was near to the abutment bearing, so
+that there was no great difference in the stress induced whether all
+three rails were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a common
+occurrence for the girders to take the full loads. The heavier engines
+passed scores of times in a day--lighter engines probably one hundred
+times. The bridge was about twenty years old, yet these cross-girders,
+when removed, showed no other sign of age and wear than that due to
+rust.
+
+[Illustration: FIG. 46.]
+
+All the foregoing instances relate to wrought-iron bridges. Two cases of
+steel construction are here added, the first of these furnishing an
+example of high girder stress somewhat remarkable. This was found in a
+trough girder of a strange pattern, of which a section is here given
+(Fig. 46). The bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a crawling
+pace. The larger of the two girders carrying the rails was 15 feet 8
+inches effective span. The sides of the trough consisted each of two
+vertical plates, originally 1/2 inch thick, but wasted to an aggregate
+thickness of 5/8 inch. These plates 6 inches deep, were connected at
+their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which
+again were riveted to a bottom plate 16 inches wide, originally 1/2 inch
+thick, wasted to 3/8 inch. Lying in the bottom of the trough, and
+riveted through the inner angle flanges, was a bridge-rail. Assuming
+that the metal retained its elastic properties from top to bottom of the
+section, at whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the net section.
+As puddled steel, of which the girders were made, may have a tenacity of
+45 to 55 tons per square inch, the assumption is probably correct. The
+author has no record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine passing over,
+required some determination.
+
+A point of additional interest in this little bridge is that, though
+made of steel, it dates as far back as 1861, having been in use
+thirty-two years when removed. The particular variety of steel used was
+known as Firth’s puddled. The evidence of this consists in
+correspondence showing that permission had been asked of the controlling
+authority, by the only users of the siding, to apply this material, with
+no evidence of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some girders of
+considerable span. The appearance of the trough girders to which the
+foregoing particulars apply was distinctly different to that which might
+be expected in ordinary wrought iron. The top edges of the vertical
+plates were wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which the girders
+held up to their work for so long is, by itself, conclusive on the
+point. The bridge-rail appeared to be of wrought iron, the different
+modulus of elasticity of which has been included in the calculation upon
+which the preceding results are based. That these girders stood so well
+is, perhaps, largely due to the fact that the load carried by them was,
+though varying within wide limits, practically free from impact, which,
+had the load passed over quickly, would, with girders so small, shallow
+and flexible, have been very sensible.
+
+The second instance of steel construction in which somewhat high stress
+is manifest is that of some steel troughing of the Lindsay pattern, used
+in a bridge built in 1885. The troughs ran parallel to the rails, having
+an effective span of 18 feet 8 inches. The depth of the section (which
+is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span
+of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.
+
+[Illustration: FIG. 47.]
+
+Assuming this to be carried on six troughs, which corresponds to 11 feet
+3 inches of width, the extreme fibre stress works out at 7·5 tons per
+square inch, under usual engine-loads. The bridge when examined after
+fourteen years’ use was in good condition, and at that time but little
+rusted; but the end seam rivets were, as is not uncommon with such
+troughing, loose. The traffic over the bridge was considerable, but not
+at great speed.
+
+On the opposite page are set out the results which have been given, in
+tabulated form, as was done for rivet stresses, to enable ready
+comparison to be made.
+
+EXAMPLES OF HIGH STRESS.
+
+  --------------+-----+---------+---------------+--------+-----------
+                |Span |  Part   |  Stress per   |Tension |Condition.
+                | in  |Stressed.|  Square Inch. |   or   |
+                |Feet.|         +-------+-------+Compres-|
+       --       |     |         | Webs  | Webs  | sion.  |
+                |     |         |  In-  |  not  |        |
+                |     |         |cluded.|  In-  |        |
+                |     |         |       |cluded.|        |
+  --------------+-----+---------+-------+-------+--------+-----------
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |60·0 |Flange   |   ..  |  6·3  |Tension | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |64·0 |   „     |   ..  |  6·8  |   „    | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |76·0 |   „     |   ..  |  7·5  |   „    | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |    {|   „     |  7·4  |  9·7  |   „    |}
+  main girders, |29·5{|   „     |  6·3  |  8·3} |Compres-|}Good.
+  plate         |    {|         |       |     } |sion    |}
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |63·0 |   „     |      7·1      |Tension | Fair.
+  lattice       |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |47·0 |Flange   | 10·0  |   ..  |Compres-| Fair.
+  plate         |     |edge     |       |       |sion    |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|26·0 |Flange   |   ..  |  6·7  |Tension | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|11.0 |   „     |  6·3  |  6·5  |   „    | Bad; loose
+  plate         |     |         |       |       |        | rivets.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|19·0 |   „     |  8·4  |  9·1  |   „    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|22·0 |   „     | 10·5  | 11·1  |   „    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Steel trough  |    {|   „     |     15·0      |   „    |}Fair,
+  girder        |15.7{|Top edge |     32·0      |Compres-|}but
+                |    {|         |       |       |sion    |}rusted.
+                |     |         |       |       |        |
+  Steel         |18·7 |Flanges  |  7·5  |   ..  |Tension | Fair,
+  troughing     |     |         |       |       |and Com-| but
+                |     |         |       |       |pression| rusted.
+  --------------+-----+---------+-------+-------+--------+-----------
+
+It would be unwise to infer from the instances which have been quoted
+that high stress may be regarded with complaisance. In the most
+conscientious engineering work there should still be a liberal margin
+for material possibly defective, or even bad, for waste and
+deterioration, and for the aggregate effect of minor errors in design,
+any one of which considerations, except the first, by itself might not
+be of great importance. The conclusion which may, however, be derived
+from this and the previous chapters is, that bridge failures are less
+likely to occur from high stress of a kind readily calculated than from
+failure in detail, obscure and little suspected, the reason for which is
+not perhaps apparent, till the attention is forcibly directed to it by
+the refusal of the structure to sustain the forces to which it may be
+liable.
+
+
+
+
+CHAPTER VII.
+
+DEFORMATIONS.
+
+
+Instructive lessons are to be had from a study of the various
+alterations in form to which metallic bridgework is liable, which
+alterations may be due simply to the development of stress of ordinary
+amount, and are then generally small; or to abnormal stresses, the
+result of some distortion in the bridge structure itself not originally
+intended, and possibly extreme. In addition to these there may be
+deformations due to settlement, to “creeping” of parts of the structure
+relative to the rest, to temperature changes, to rust, and to original
+bad workmanship. In any instance quoted below the methods adopted to
+ascertain the amounts of such alterations were quite simple, even crude;
+but as care was exercised, and no attempt made to measure any very
+minute changes, the results may be accepted as practically correct.
+
+Dismissing for the present changes of form such as are to be expected,
+and touched upon in other places in this work, with respect to the
+particular parts of bridge structures affected by them, a few instances
+will be adduced of alterations which, though not very surprising, are
+such as in the design of the work are hardly likely, in most instances,
+to have been contemplated.
+
+A case has already been referred to in which, owing to eccentric loading
+of main girders, these were, as to the top flanges, flexed sideways a
+considerable amount. It is proposed to supplement this by further
+remarks relative to somewhat similar cases. A like effect is frequently
+to be observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting ledges
+formed by the bottom angle-bars of such troughs. In old forms of this
+arrangement it is common to find the two girders forming the trough
+connected only by bolts passing through the timbers, or just above them
+and below the rails; or connected by narrow strips, which serve no other
+purpose than to prevent the sides spreading at the bottom. The top
+flanges in such cases commonly curve inwards on the passage of the
+running load, accompanied of necessity by an increase of compressive
+stress upon the outer edges of the flanges, and perhaps by the working
+of any flange-joint which may exist. This, both as to flexing of the top
+flange and the working of a joint, was noticed in the case of a bridge
+twenty-three years old, very similar to that illustrated in Figs. 8 and
+9, and described on pages 13 and 14. The top flange consisted, however,
+of a bridge rail riveted to the top edge of the web, butting at a joint,
+and covered by thick cover strips (see Fig. 48). The joint itself was
+poor, and depended largely upon the character of the butt, which was not
+sufficiently good to prevent the top member kinking at this point, under
+the joint influence of transverse effort and compressive stress, with
+possibly some help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked in passing that it is
+very objectionable to use bolts as was done in this instance; for as the
+timber settles down on its seat, taking the bolts with it, these bear
+hard in the webs, enlarging or even, as in this case, tearing the holes,
+accompanied by injury to the bolts themselves. The practice is now
+almost obsolete, but the example is instructive as showing the
+impropriety of securing timbers by bolts passing through them at right
+angles to the action of the load, unless these bolts are quite free to
+move with the timber as it compresses.
+
+If trough girders must be used, the better plan is to connect the two
+sides by a continuous bottom plate, the trough thus formed being
+properly drained, if the timber is not bedded in asphalt concrete; or to
+introduce stiff diaphragms at intervals beneath timbers, if the depth
+suffices.
+
+In the case just quoted the curvature of the top members of the girders
+was inwards, but in the instance given below, of twin girders 26 feet
+effective span, with longitudinal timbers between, resting, as before,
+upon the inner ledge formed by the bottom flanges, the curvature was
+observed in three out of four girders to be 1/2 inch in a contrary
+direction, the fourth remaining straight.
+
+[Illustration: FIG. 48.]
+
+[Illustration: FIG. 49.]
+
+An inspection of the accompanying section, Fig. 49, will, perhaps,
+render the reason evident when it is noticed that the top members are
+very unsymmetrical in form, the effect of this being to give these
+members, under stress, a strong tendency to flex outwards, apparently
+more than sufficient to counteract the tendency of an eccentric
+application of load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be not
+materially in excess, and is actually so, only because the thinness of
+the web--1/4 inch--renders it incompetent to keep the bottom flange up
+to its work, and so secure the full effect of the eccentric loading in
+limiting the outward tendency, due to the section of the top member,
+the effects of which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange to the other
+prevent the want of symmetry noticed in these--which, by the way, is on
+the wrong side for utility--from having any particular effect.
+
+To give one other example of the consequences of eccentric loading, a
+bridge of 48 feet effective span may be quoted. This bridge carried four
+lines of way supported by five main girders, trussed by kicking-struts
+in such a manner as to form a bastard arch. A part section and plan are
+given in Figs. 50 and 51.
+
+[Illustration: FIG. 50.]
+
+[Illustration: FIG. 51.]
+
+The floor consisted of Lindsay’s troughing resting upon the lower
+flanges of the main girders, the three middle girders, subject to
+eccentric loading, sometimes on one side, sometimes on the other, were,
+with dead load only, straight; but the two outer girders, liable to
+loading only on one side, had, under repeated applications of such a
+load, assumed a permanent curve towards the rails--13/16 inch in one
+case and 1 inch in the other--which curvature, no doubt, increased when
+a live load came upon the contiguous roads, though this was not
+measured. It should be remarked in passing that, owing to settlement and
+the canting of the abutments, the three middle girders were also
+“down”--in one case 3/4 inch. The girders, with one near road loaded,
+deflected 1/8 inch--greatly less than would have been the case had the
+main girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.
+
+Deformations due to settlement may be very considerable. The author
+recalls two instances affecting continuous girders. In the first of
+these, a bridge twenty years old, of two spans of about 50 feet each,
+and with girders 4 feet 6 inches deep, the centre pier had sunk 4
+inches, reducing the spans, as respects the dead load, practically to
+the condition of simple beams, just resting, but hardly bearing, upon
+the piers when free of live load.
+
+In the second case, also of two openings of about 55 feet each, with
+girders 8 feet deep, one abutment had sunk about 3 inches, more than
+doubling the stresses over the centre pier. It is manifest that
+continuous girders should only be adopted where settlement of the
+supporting points is not likely to occur to any material degree. If this
+cannot be relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to make a liberal
+allowance for settlement stresses, in which case any economical
+advantage that should exist will probably disappear. It is, however, to
+be acknowledged that so long as the girders are in touch, under dead
+load, with the bearings intended to support them, the stresses due to a
+live load are unaltered, the principal effect in this case being that
+the variation in stress due to the live load ranges between limits that
+are higher or lower in the scale of stress than is the case with
+bearings undisturbed; still, if it is desired that the maximum stress
+shall not exceed, say, 6 tons per square inch, it can hardly be a matter
+of indifference that settlement shall induce a maximum of, perhaps, 10
+tons, as in that case the stress must be 4 tons nearer the limit of
+statical strength.
+
+Before leaving this matter it may be well to point out that in the case
+of continuous girders of uniform section a moderate settlement of the
+piers may even be advantageous by reducing the moments over the piers,
+and possibly making them equal to those obtaining near the middle of the
+spans, in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.
+
+Bridges consisting of simple main girders connected by cross-girders may
+be very prejudicially affected by unequal settlement; for instance, if
+one girder bearing settles more than the others, a twist is put upon the
+structure very trying to the floor-girder connections, and possibly to
+the main girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments. Indeed,
+settlement of this kind may be much more destructive to a metallic
+bridge than to an arch of brick or masonry, the commonly accepted
+opinion notwithstanding.
+
+Instances of deformations due to the creeping of some part of the
+structure away from its work, are within the author’s knowledge, rare;
+except in the case of the ends of main girders in skew bridges, already
+referred to.
+
+Distortion, the result of temperature changes, is frequently to be
+observed in any considerable length of girder flange or parapet where
+there is not freedom of movement, unless due provision is made to check
+it.
+
+It is quite common to see parapets out of line, either because the ends
+are not free, or because the light work of the parapet being more
+exposed to the sun’s rays than the girder work to which the lower part
+is attached, expanding to a greater degree, is subject to considerable
+compressive force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or flexible
+joints at moderate distances apart, or to make the parapet sufficiently
+stiff to take the stresses developed, without crippling. A parapet may
+also go out of shape if directly attached to the top flange of a girder
+liable to heavy loading, particularly if the girder be shallower than
+the parapet, simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the girder
+proper.
+
+Rivets spaced too far apart, by allowing the plates or other parts to
+spring open slightly, and permitting moisture to enter, results in the
+growth of rust, which, as it swells in forming, forces the parts
+asunder, and may set up considerable stress.
+
+Flat bars riveted together by rivets spaced 12 inches apart may from
+this cause be forced asunder, as much as 1/2 inch, sufficient to set up
+a stress, with any practicable thickness of bar, much exceeding the
+elastic limit.
+
+Local distortions may occur as the result of imperfect workmanship or
+careless erection, causing quite possibly very severe local stresses; or
+girder flanges may be out of straight as a result of riveting up along
+one side first, instead of advancing the riveting simultaneously along
+the whole breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is sometimes
+done to girderwork during manufacture by rough treatment to make the
+work come together; but the author has little to offer with respect to
+these matters that is not common knowledge. It may, however, be pointed
+out in passing that a bridge upon the design of which great care has
+been expended, with the idea that theoretical propriety shall not be
+violated, may be completely spoiled in this respect by careless
+construction. Fortunately, both steel and wrought iron, if of good
+quality, are long suffering. Incompetent erection will sometimes result
+in the true girder camber not appearing, or in differences as between
+girders supposed to be similar. This is not, of course, a deformation in
+the sense in which the word has previously been used, but it is
+desirable to bear the fact in mind as a possible cause of defective
+camber in dealing with questions of deformation.
+
+The foregoing has reference chiefly to alterations of form in bridgework
+of wrought iron or steel, but a case of considerable interest is that of
+a cast-iron arched structure, of which the author made a very complete
+examination.
+
+[Illustration: FIG. 52.]
+
+[Illustration: FIG. 53.]
+
+This bridge, built in 1839, and carrying two lines of railway, consisted
+of three spans, 100 feet each, of 10 feet rise, made up of four inner
+and two outer ribs, each rib being in three nearly equal parts; the
+floor was of timber, the abutments and piers of masonry. As originally
+constructed there was no bracing between the ribs other than the frames
+indicated on the plan here given (Fig. 52), stretching from outer rib
+to outer rib in the neighbourhood of the rib joints, which were simple
+butts without bolts or any equivalent means of connection. The floor
+was, however, braced in the horizontal plane, and the structure was also
+braced over the masonry piers. After forty-two years’ use supplementary
+distance-pieces were introduced between the ribs, but still no bracing
+between them, or any efficient means of checking lateral movement. A
+crack developing in one of the outer ribs at the crown, led to an
+investigation to trace the cause, the bridge then being fifty-four years
+old. Careful plumbing of the abutments revealed the fact that three out
+of four abutment pilasters were out of the vertical, as shown in Figs.
+52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner
+from which the cracked rib had its springing; there was also other
+evidence of settlement in an old crack extending from the top of the
+abutment to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were also out of
+plumb, that which was cracked being 2-1/2 inches out at the centre. The
+joints of the ribs, which, as already stated, were simple butts, in some
+cases opened and shut, as the load passed over, in such a way as to
+suggest that the ribs were acting, in a manner, as four-hinged arches,
+of which two hinges were at the springing, and the other two at the
+joints, one of which would for most positions of the load be out of use,
+reducing the rib to the three-hinged condition; in other words, as the
+rolling load passed over the span, one or other of the two joints of a
+rib would “gape” an appreciable amount at the bottom or at the top.
+Observations were taken by means of a theodolite placed below, either
+upon the bank or upon the tops of the masonry piers, sighting upon
+suitable scales attached to the ribs to ascertain the amounts of
+vertical and horizontal movement during the passage of trains over the
+bridge. The principal results are set forth in the following table:--
+
+MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT.
+SPANS.
+
+  ----------------------+-------+----------+-----------
+                        |Fall in| Rise in  | Lateral
+            --          |Inches.| Inches.  | Movement
+                        |       |          |in Inches.
+  ----------------------+-------+----------+-----------
+                      _Span No. 1._
+  At A. Up road loaded  |  ·20  |   ·08    |   ·04
+   „ A. Down road loaded|  ·08  |   ·03    |   ·04
+   „ B. Down road loaded|  ·14  |No record.|   ·02
+                      _Span No. 2._
+  At C. Up road loaded  |  ·40  |   ·13    |  Slight.
+   „ C. Down road loaded|  ·10  |   ·05    |     „
+                      _Span No. 3._
+  At D. Up road loaded  |  ·22  |No record.| No record.
+   „ D. Down road loaded|  ·15  | Slight.  |  Slight.
+  ----------------------+-------+----------+-----------
+
+  NOTE.--The lateral movements are to either side of the mean position.
+
+The particulars for spans 2 and 3 were obtained with the instrument set
+up on the pier between these spans. The tremor of this pier was such
+that no useful readings for lateral movement could be obtained. Further,
+as the rolling load came upon these spans, the effect was to rock the
+pier to an extent vitiating the readings for vertical displacement; but
+by sighting upon the fixed abutment, and observing the amount of this
+rocking, suitable corrections were made in the apparent rib movements.
+The figures given in the table are thus corrected. The pier rocking was
+equivalent, as an extreme, to an inclination from the vertical of 1 in
+3200. An attempt to measure the horizontal movement of the pier-top was
+unsuccessful, owing to the impracticability of setting up the instrument
+in a suitable position, sufficiently near to the pier to enable readings
+to be satisfactorily taken. This horizontal displacement probably
+amounted to about 1/16 inch either way. The rise and fall of the arches,
+and rocking either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect to the
+spans. Summarising the results, the greatest vertical movements
+downwards were 0·20 inch, 0·40 inch, and 0·22 inch for spans Nos. 1, 2,
+and 3, the upward movements being 0·08 inch and 0·13 inch for the first
+and second spans, there being no recorded result of this kind for the
+third span. With adjacent ribs loaded, the movement of the ribs unloaded
+was one from one-third to one-half of the full amounts. It is to be
+noted that the lateral displacement in no case exceeded 0·04 inch either
+way, nor were the vertical movements exceptional; yet, as a matter of
+sensation, when seated upon the ironwork, it was a little difficult to
+believe them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0·45 inch, 0·45 inch, and 0·55
+inch for the spans in order, the extreme temperatures being fairly
+representative of the English winter and summer. The structure was, as a
+consequence of the examination, efficiently braced by diaphragms between
+the ribs, and diagonals following the arch ribs round from springing to
+springing, with satisfactory results. The crack already referred to, and
+its probable causes, will be dealt with under “Cast-Iron Bridges.”
+Eventually this bridge was reconstructed to meet the requirements of
+growing engine-loads.
+
+
+
+
+CHAPTER VIII.
+
+DEFLECTIONS.
+
+
+Deflection, considered only as a fraction of the span, and without
+regard to other conditions affecting it, is of very little use as an
+indication of a girder’s fitness for its work; but when taken with
+reference to the depth of the girder, the nature and amount of the load
+producing flexure, and, further, with regard to the quality of the
+workmanship and normal properties of the material of which the beam is
+constructed, it may be of some little service in helping to form a
+reliable opinion. This consideration applies with less force, perhaps,
+to new work than to old, in which there may be unknown influences at
+work, or unknown defects which by excessive deflection may be betrayed.
+Though too much importance should not be attached to results of
+deflection tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each case, gives a
+good general idea of what may be expected in a fresh instance, any
+material departure from which should be a reason for specific inquiry as
+to the cause. A further reason with new work is found in the evidence it
+affords as to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case of floor
+beams, in what way the load is distributed amongst them, if, indeed,
+there be any such distribution.
+
+The author has commonly found that new work gives greater deflections
+than old--i.e., while calculation gives the same result for each, it
+does not apply equally well to both. The differences may be accidental,
+but are probably due to other causes, perhaps to the fact that new work
+has not by repeated applications of load lost the resilience of parts
+liable to considerable local stress, such as is very liable to occur at
+connections, so that the deflection is, whilst new, greater than after
+many years’ use, by which time such parts may develop a definite “set,”
+and contribute in a less degree, or not at all, to the total elastic
+deformation.
+
+It is also possible, as already suggested, that repeated high stress may
+reduce the ratio of strain to stress, the material gradually becoming
+more rigid, the modulus of elasticity being, in fact, increased.
+
+In girders of ordinary construction, the major part of the deflection is
+due to the booms, the remainder to the web; the latter is for plate
+girders a small amount only, and is commonly neglected, but for open web
+constructions it may be quite appreciable. For any given type of web
+arrangement the deflection due to the web will, for all depths, remain a
+constant quantity for the same span and unit stress; and though a
+moderate fraction of the whole deflection for a shallow girder, it may
+be a very considerable part for a girder of great depth, in which that
+part due to the booms is, of course, smaller, since the deflection due
+to these varies inversely as the girders’ depths.
+
+Deflection, being dependent upon the elasticity of the material, is of
+necessity very largely influenced by the value of its modulus E, itself
+liable to considerable variation, and is increased in a small degree by
+the yield of joints and rivets, which effect, apart from the initial
+“set” of the girders, appears to be negligible. The stiffness of members
+in resisting angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less, and,
+finally, section excess at joints and gusset attachments has an
+influence in modifying deflection as compared with that due to the
+normal gross sections simply.
+
+From these considerations it is apparent that any simple deflection
+formula must be largely empiric in its nature. For plate girders of
+uniform depth and flange stress, the writer has found the following to
+give good results:--
+
+   S^2
+  ----- × _f_ = deflection in inches.
+  D × C
+
+The span S and depth D are, as a matter of convenience, taken in feet;
+the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is
+the mean of the extreme tensile and compressive stresses of the booms,
+in tons per square inch, estimated upon the gross sections.
+
+This, though satisfactory for plate girders, is not so suited to girders
+having open webs, in which the deflection will more nearly be
+
+  (3S    S^2 )
+  (-- + -----) × _f_,
+  (C    D × C)
+
+the constant C being 3900 and 4450 for iron and steel respectively. The
+latter values of C correspond to normal values of the modulus of
+elasticity of 11,700 and 13,350 tons for iron and for steel, it being
+assumed that any slight rivet yield is off-set by any small section
+excess--say, 5 per cent.; it may, however, happen that section excess is
+greater than assumed, in which case some allowance may properly be made
+for this by increasing C.
+
+To adapt the formulæ to girders other than those having parallel booms
+and uniform stress, the results, as deduced above, may be multiplied by
+constants given in column B of the Table given on page 93.
+
+The practice of adopting for E in deflection formulæ a quantity much
+smaller than its nominal amount, with the object of allowing in riveted
+girder work for the yield of rivets and of joints, can hardly now be
+defended, whatever may have been a case at a time when workmanship was
+much inferior, when there was no machine riveting, and joints were,
+owing to the small weight of plates and bars, three times as numerous.
+
+The initial “set” of a girder consequent upon first loading is a
+quantity quite distinct from deflection proper, and may be so small as
+to be negligible, or read 10 per cent. of the true deflection, varying
+with design and workmanship.
+
+No estimate of girder deflection can be even approximately true if there
+is, at the level of the top or bottom flanges, a plated or otherwise
+rigid floor system which is not taken into account, as this will have
+the effect of very materially reducing the boom stress. To neglect this
+influence, where it exists, must necessarily lead to disappointing
+results, and it is quite practicable in many instances to include it in
+the calculation.
+
+The influence of angular distortion between the various members has been
+neglected. It may be pointed out, however, that the resistance
+accompanying these movements in girders having riveted connections,
+though unimportant as affecting deflection, is worth some consideration
+in regard to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount for any span,
+but will generally be of less importance in large girders than in small,
+because in large girders the ratio of the breadth of members to their
+length is commonly less.
+
+When determining the probable deflection of any girder of exceptional
+figure, it will be found convenient to make a strain diagram--an old
+device, in which the actual alterations of length being ascertained for
+all members, the girder is carefully set out to a suitable scale, with
+the lengths of members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the probable
+deflection. The value of E for this purpose should never be taken at
+less than the normal amount, and may for a considerable excess of metal
+in joints and gussets be made as much as 10 per cent. greater, this
+being a convenient means of making the necessary correction.
+
+The effect of loads quickly applied may here be considered in connection
+with elastic deformations of girders of the same span, but different
+depths. If these be designed for similar loads and unit stresses, the
+deflections due to webs and booms of the girders compared will bear the
+same relation, each to each, as do the weights, whether in both cases
+the loads be inert or quickly applied, from which it follows that the
+mechanical “work” done by the loads in falling through the deflection
+heights is, neglecting inertia, always in proportion to the girderwork
+weights, and is a similar amount per ton, which as the total length of
+members remains substantially unaltered, corresponds to a similar amount
+of work per unit of section, or similar stress, irrespective of the
+depth of the girders.
+
+But for a “drop” load, as when there is some obstruction upon a railway
+bridge, there will be in addition a further amount of work to be
+absorbed, which is to be considered the same whatever the girder’s
+depth, and will for deep girders be a larger amount per ton of
+girderwork than in those that are shallow; this, taking effect on
+members of the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in the booms.
+
+The influence of the girder’s inertia in modifying drop-load effects
+will also be less marked in deep--i.e., light--girders than in girders
+shallow and heavy.
+
+It is, notwithstanding all this, desirable that the depth of main
+girders should be liberal for economy’s sake, and also that of floor
+beams, for reasons already dealt with; the probability of the drop load
+is somewhat remote, and, though possible, would simply induce, if it
+occurred, an increment of stress rather more important in deep girders,
+making it specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact effects.
+
+It should be remarked that for short and very flexible beams, generally
+outside the limits of practice, there may also be, under quickly moving
+loads, a material increase of stress due to the centrifugal effort of
+the load on running round the deflection curve, and in rising upon the
+steep part of the curve beyond the girder’s centre. Where advisable,
+these effects may be modified by cambering the rail.
+
+For pin bridges in which there may be spring in the pins, excess stress
+in some eye-bars due to inequalities of length, and a want of that
+rigidity peculiar to riveted structures, the deflection will be greater
+than above indicated for girders of the ordinary English type.
+
+The method in common use for measuring the deflections of girders but a
+moderate distance above the ground by means of sliding-rods, though
+crude, gives, with care, results sufficiently accurate for most
+practical purposes; but some points necessary to remember may be
+mentioned with propriety. The lower rod should rest firmly upon
+something solid, say a stone, well bedded and free from any tendency to
+rock; the upper end should bear against some part of the girder above,
+presenting a hard surface, free from dirt or scale, and as the running
+load approaches the bridge it should be ascertained that there is no
+slack, that the rods bear hard at the top and bottom. The upper end
+having been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other. These
+precautions are so self-evident that an apology is almost necessary for
+mentioning them.
+
+To ascertain deflections with a single pair of rods is only allowable
+when the girders rest firmly on their bearings; if felt has been placed
+under the girder ends, or if the bedstones are insecure or rocking, it
+is necessary to use three pairs of rods, one pair at the middle and a
+pair at each end, in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the desired
+result.
+
+In the case of a number of spans in series, each resting upon sill
+girders common to two sets of bearings, this method also gives results
+of indifferent reliability, as the depression of each end may be greater
+as the travelling load comes upon and leaves the span than when it is
+precisely over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular position of
+the running load, which are what is required.
+
+The author suggests, as a means of ascertaining deflections free from
+these objections, that it should be done by first measuring the slope at
+one end, and from this deducing the deflection at the centre.
+
+This is to be accomplished by means of a little instrument, consisting
+of a telescope with cross-hair sights, and fitted with a reflecting
+prism at the eye-piece capable of being turned round, so that the
+observer has a wide choice as to the position he assumes with reference
+to the instrument, and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one end of the
+girder over the bearing, at the other end a scale is secured, to which
+the telescope is directed, the cross hair being made to sight on the
+zero of the scale, or the reading noted. For a girder supposed to
+deflect to uniform curvature (say, with uniform depth and uniform
+stress, the ordinary case) the reading observed will be four times the
+deflection; every 1/10 inch actual reading on the scale will correspond
+to 1/40 inch of girder deflection.
+
+Apart from the deflection, this method gives a ready means of observing
+the end slope, a quantity of equal value for purposes of comparison. As
+with girders of similar proportions, and similarly stressed, the
+deflection will at all spans be the same fraction of the span; so should
+the end slope be a constant quantity under similar conditions, the
+diagram, Fig. 54, will make the principle quite clear.
+
+[Illustration: FIGS. 54 to 57.]
+
+Strictly the character of the deflection curve is slightly modified by
+that part of the deflection due to the web; so that the depression at
+the centre would, in the case assumed above, be somewhat more than
+one-fourth part of the end reading, and generally will be a larger
+fraction of the reading than that deduced from a consideration of flange
+stress simply. In Figs. 55 to 57, which are intended to explain this,
+it will be noticed that deflection due to the web is shown
+straight-lined from the bearings to the centre of the girder; this is
+strictly true only for a girder correctly designed for an immovable
+distributed load; but as there should be for girders intended for a
+travelling load, some excess in web members near the centre under the
+condition of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as shown in the
+diagram for the sake of simplicity.
+
+Suitable constants, including the corrections necessary, are given in
+column A of the table annexed for a few typical cases, and by these
+constants the actual readings should be multiplied to find the
+deflection. The constants have been worked out for depths of one-tenth
+the span; for greater depths they should be slightly more, and for
+smaller depths somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly exceeding 5
+per cent., and generally much less.
+
+The figures in column B relate to the formulæ previously stated, and
+apply equally well to all depths.
+
+TABLES OF MULTIPLIERS FOR DEFLECTION.
+
+  _Uniform Stress_:                                           A.     B.
+      Girders of uniform depth, varying flange section       0·27   1·00
+      Hog-backed girders, ends half of centre depth, varying
+      flange section                                         0·24   1·08
+  _Varying Stress_:
+      [1]Girders of uniform depth and flange section         0·32   0·87
+      [1]Hog-backed girders (as above), but uniform flange
+      section                                                0·29   0·97
+      [1]Bow-string girders of uniform flange section        0·16   1·30
+
+[Footnote 1: For uniform loading.]
+
+It is apparent that, if preferred, the scale, instead of being in
+inches, divided suitably, may, for each type of girder, be amplified to
+the proper degree, so that the amount of the deflection may be read off
+at once.
+
+This method of dealing with deflections is quite independent of the
+character of the bearings, and is applicable to girders at any height
+above ground or over water; but its use would hardly be practicable for
+very small beams, or those in an awkward position, or near which it
+would be impossible to remain with a running load upon the bridge.
+
+There is a possible source of error in the use of the instrument, most
+likely to occur with triangulated girders, with which, if the instrument
+is placed at the top of an end post, the reading observed may be the
+joint effect of deflection and of local flexure of the members meeting
+near the telescope. This may be tested, and, if necessary, allowed for,
+by first sighting upon a scale at the next apex, and observing the
+effect of the moving load. Again, as girders sometimes cant towards the
+running load, if the instrument is placed on one edge of a girder, and
+the cantings of the two ends are dissimilar, a false reading will
+result, which may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between the cants
+upon the observation. Only in exceptional cases is it likely that either
+of these considerations would need attention.
+
+The author has secured with this instrument very promising results,
+notwithstanding that under a running load there is a slight haziness of
+the scale as seen through the telescope, due to “dither,” largely the
+result of imperfections which may be remedied.
+
+Deflections may sometimes be conveniently taken, by a quick-eyed
+observer, with a good surveyor’s level and a specially-divided staff
+held at the centre of the girder. The divisions preferred by the author
+for this purpose are 1/10 inch, plainly marked, which may be seen at 50
+feet distance with sufficient clearness to make possible readings by
+estimation between the divisions to, say, 1/50 inch. But it is clearly
+desirable not to rely upon a single observation only, where all the
+evidence is gone so soon as the sight has been taken.
+
+In rail-bearers, or other short girders, it may not be practicable to
+adopt such methods, either on account of an inability to find a suitable
+place for the instrument, or to read with any telescope with sufficient
+promptitude as the load passes rapidly over. The use of rods may also be
+out of the question, as the errors attending their manipulation may be
+serious where but a small movement has to be noted, this being
+complicated in some instances by the bearings being insecure, and
+working to an extent which obscures the measurement sought. In such
+cases it is preferable to use a stiff slat lying along the girder, which
+bears, through short blocks over the girder bearings, upon the flanges;
+the deflection is then read by direct measurement of the girder’s
+depression at the centre, relative to the slat.
+
+The author is, unfortunately, not able to give any precise information
+on the effect of running-load as against a load that is stationary in
+connection with girder deflections. It is by no means easy in ordinary
+work upon a railway to secure facilities for making such comparative
+tests. It may, however, be confidently stated, as a result of such
+observations as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a 50 feet
+span, but little greater than that due to the same load stationary; it
+may be, perhaps, 5 to 10 per cent. more.
+
+It is evident that to determine the precise difference where the
+quantity to be measured is so small needs apparatus of a more delicate
+character than that in common use, and the control of an engine, or
+engines, for the purpose of making the special tests, conditions which
+on a busy line can only be secured by special arrangements previously
+made.
+
+
+
+
+CHAPTER IX.
+
+DECAY AND PAINTING.
+
+
+The author has collected particulars as to the amount and rate of
+rusting in metallic structures which are of some interest. In all such
+instances it is very necessary to note the conditions which have
+obtained during the process of wasting, as without this, misleading
+conclusions may be drawn. The information given relates in all cases to
+wrought iron, unless otherwise stated.
+
+A plate-girder bridge, having girders under rails, was found to be badly
+rusted. The atmospheric conditions were unusually trying, the air being
+damp and impregnated with acid fumes from adjacent steel works. That the
+wasting was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than those
+farther removed and partly sheltered from the corrosive influence.
+
+The webs were in places eaten right through, having lost a mean amount
+of about 1/8 inch full on each surface in twenty-eight years. Painting
+had not been well attended to.
+
+In a similar bridge, not a great distance from this, but sufficiently
+far away to modify the conditions for the better, considerable wasting
+was also observed, but more particularly where the girders had been
+built into masonry, which, loosening with the constant movement of the
+girder-ends, had allowed moisture to collect, and rust to develop,
+without the chance of repainting these surfaces. The amount of waste at
+the places indicated was, as in the last case, about 1/8 inch on each
+face, and in the same time, other parts of the girders having suffered
+less.
+
+[Illustration: FIG. 58.]
+
+A third plate-girder bridge, with outer main girders, cross-girders, and
+plated floor, carrying a road over a railway and sidings, and which was
+known to have been neglected in the matter of painting, was very badly
+rusted, both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration was, however, the
+smoke and steam from locomotives, which frequently stood for some time,
+during shunting operations, directly under the bridge. The webs of the
+cross-girders, which were originally 1/4 inch thick, had rusted into
+occasional holes during fourteen years--i.e. 1/8 inch from each surface
+in that time. When removed a little later the wasting was so complete
+that it was possible to knock out with a light hammer the remains of the
+web between flanges and stiffeners, so as to leave an open frame only.
+One of the cross-girders was so treated by the men engaged upon the
+work, when it presented the appearance shown in Fig. 58.
+
+In another case--that of a bridge with lattice girders under rails--the
+ends were built into masonry, which had, of course, loosened, with the
+usual result. The air of the locality was certainly pure, but somewhat
+damp. The general condition of the ironwork was good, but end-bars of
+the diagonal bracing, where they had been closed in, had lost 1/8 inch
+on each surface in thirty-three years. The top flanges immediately under
+the timber floor were in a very fair state, which is of some interest
+when it is considered that these were made of steel of the same kind as
+that already noticed as being used in the construction of small girders
+(see Fig. 46, _ante_), described in the chapter upon “High Stress,” both
+cases dating from the year 1861. The painting upon the lattice-girder
+bridge had been pretty well attended to; but in the case of the small
+steel girders it had been greatly--perhaps altogether--neglected; this,
+coupled with adverse atmospheric conditions, had produced the result
+that the rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully 1/8 inch on
+each surface, as against a negligible amount under the more favourable
+circumstances.
+
+Girder-work over sea-water, as in piers, seems to rust at a sensibly
+greater rate than inland work under average conditions; but it is hardly
+practicable to make any strict comparison, as in either case the rate of
+oxidation is so much affected--even controlled--by the care bestowed
+upon the structures. This general conclusion is based upon the results
+of examination of wrought-iron girder-work over sea-water of ages
+varying from fourteen to forty-four years. It should be remarked,
+however, that in one case steel girders but five years old, and which
+were frequently wetted with sea-spray, were found to be wasting rather
+badly--the paint refusing to keep upon the surface.
+
+It may be concluded from the above instances, and from others which have
+come under notice, that wrought-iron work, if not properly cared for in
+respect to painting, or under conditions otherwise bad, may be expected
+to rust at a rate which corresponds to the loss of 1/8 inch on each
+surface in from fifteen to thirty years; but with proper care as to
+painting, and exclusive of exceptionally bad conditions, it does not
+appear to waste at any measurable rate. In some instances, upon scraping
+the paint from girders which had been in use for thirty years, the
+author has found, beneath the original red lead, the metallic surface
+bright and clean, showing no trace of rust.
+
+Of ordinary steelwork the same cannot be said, the common experience
+being that mild steel is very liable to be attacked by rust. With
+passable care in the bridge-yard during manufacture, such that with
+wrought iron no after-trouble would be noticeable, steel is very liable
+to show, within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away discloses a
+small rust-pit. This is more often seen on the flange surfaces
+(horizontal) than on web surfaces (vertical), but it is probable the
+position has little to do with the matter, and that it is rather due to
+the fact that rust has been earlier started on the flange-plates, upon
+being put through the drilling-machines and inundated with slurry, which
+occurs only to a more limited extent with webs having fewer holes. The
+heads of steel rivets do not show this tendency to “pit,” or to early
+development of rust. The riveting is about the last operation in making
+a girder, each rivet being freed of all rust by heating, and quickly
+coming under the protection of oil or paint. It may happen in this way
+that the heads of rivets on a girder may be exposed without protection
+for as many hours only as the rest of the work for weeks, which fully
+accounts for the difference in behaviour.
+
+The essential point to be observed in all steelwork is to prevent, if
+possible, the first development of rust, for once begun it is much more
+difficult to arrest than in iron; for this reason, oiling of all
+material for a steel bridge, at a very early stage of its existence,
+cannot be too strongly insisted upon. This practice, however, makes the
+work so objectionable, and even dangerous when being lifted--because of
+the liability to slip--to the men engaged upon it, that it is commonly
+very difficult to ensure it being done sufficiently soon to satisfy a
+careful inspector. If the work is carried out under cover, the
+requirement is less urgent. Strictly, all material should be oiled so
+soon as rolled, but the author does not remember to have seen this done
+at any of the mills he has visited, though it is common enough to find
+it specified.
+
+Ironwork does not need the extreme care which should be bestowed upon
+steelwork, but it is desirable that it should be painted as soon as
+possible, the surfaces being first thoroughly cleaned.
+
+There is, probably, for painting girder work nothing to beat good red
+lead as a protective coating; but there is considerable difficulty in
+getting it reasonably pure, without which quality its utility will be
+greatly reduced. The question of purity will, however, be found to be
+largely a question of price. It may be stated broadly that, whether for
+steel or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.
+
+In repainting old work, care should be taken to remove all traces of
+rust previous to laying on the new coat. It is not an altogether
+uncommon practice to repaint old structures by dealing only with the
+parts readily accessible, which, being less liable to rust, probably but
+little need it; leaving those parts which are difficult of access, and
+where rust is developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said, is
+indefensible. It is better rather to neglect the surfaces freely exposed
+and ventilated, and devote the whole care upon those other parts,
+confined and difficult to get at; taking the trouble necessary to remove
+ballast, timber, or whatever may obstruct the operation, in order that
+the bad places may be thoroughly scraped, and then painted. Those parts
+which most need attention may cost, perhaps, to reach--and deal with
+when exposed--ten times as much per yard of surface as the rest of the
+superfices, which needs little, and is always accessible; but the cost
+should not deter the proper carrying out of the work, as it will prove
+the very worst sort of economy to deal with painting in a perfunctory
+manner.
+
+It should be noted that girder work, whether of wrought or cast iron,
+when embedded in lime or cement concrete, or mortar, generally proves to
+be very well preserved, provided that close contact has obtained.
+Cast-iron girders, when carrying jack arches resting upon the bottom
+flanges, are found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of new
+girders. Much the same remarks apply to girders of wrought iron carrying
+jack arches, where protected by the brickwork; provided that the girders
+are sufficiently stiff to minimise deflection, and allow the masonry or
+brickwork to adhere to the surfaces.
+
+Such girders are in a very different condition to those previously
+referred to, in which the ends of the girders, carrying a light floor
+structure, are built into masonry where the deflection slope is
+greatest; though, apart from the few cases where adherence can be relied
+upon, building-in is an undesirable practice, and has the disadvantage
+that after-examination is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted to.
+
+Cast iron has ordinarily--unlike wrought iron or steel--great capacity
+for resisting rust, and will, after many years of absolute neglect,
+appear but little the worse; an advantage which is the more pronounced
+when considered relatively to the greater thickness of the thinnest
+parts in cast-iron girders, the percentage of waste being
+proportionately lessened.
+
+Cast iron does, however, behave somewhat badly in sea-water, the metal
+sometimes losing its original character, and becoming in time quite
+soft; though, if not worn away, as by the attrition of shingle,
+maintaining its original bulk.
+
+Of some forty-five cast-iron piles belonging to various structures,
+examined whilst engaged upon sea-pier work for Mr. St. George-Moore,
+though the author found somewhat diverse results, in no case did there
+appear to be any general softening of the whole thickness, but a
+distinct change for some definite distance inwards, generally to be
+decided without difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of softening was
+found close to the ground, this depth rapidly decreasing higher up,
+till, at a height of 5 feet, but little if any softening could be
+detected. At 2 feet above ground the softening was frequently but
+one-quarter of that at ground level. There was, too, often a
+considerable difference in the behaviour of different piles in the same
+structure under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly none at
+all. For six different structures the amount of softening near ground
+level, of about twenty-five piles examined, was as given in the table on
+the next page.
+
+The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot
+above ground, in a pile thirty-six years old. The decayed material when
+removed was of a soft, greasy consistency, perfectly black, which a few
+hours later was found to have changed to a dry yellow powder, by the
+rapid absorption, it may be supposed, of atmospheric oxygen. It is
+apparent, therefore, from this example that deterioration may proceed to
+a considerable depth; but it should be observed that other piles of the
+set showed softening at ground level of 1/8 inch only.
+
+SOFTENING OF CAST-IRON PILES IN SEA-WATER.
+
+  ---+--------+----------+-----------+----------+---------+---------
+  No.|  Age.  | Maximum  |  Maximum  |Mean Rate | Quality |Materials
+     |        |Softening.|  Rate of  |    of    |of Metal.|Entered
+     |        |          |Softening. |Softening.|         |by Piles.
+  ---+--------+----------+-----------+----------+---------+---------
+  1  |17 years|5/16 in.  |1/8 in. in |1/8 in. in|Soft     |Extremely
+     |        |          |7 years    |15  years |         |soft
+     |        |          |           |          |         |sandstone.
+  2  |36 years|9/16  „   |1/8 in. in |No result |  „      |Rubble
+     |        |          |8-1/2 years|          |         |mound.
+  3  |32 years|3/8   „   |1/8 in. in |1/8 in. in|Moderate-|Fine
+     |        |          |11 years   |15  years |ly hard  |sand.
+  4  |38 years|1/10  „   |1/8 in. in |1/8 in. in|Hard     |Extremely
+     |        |          |47 years   |140 years |         |hard rock.
+  5  |17 years|Small     |Negligible |          |(?)      |Sand and
+     |        |          |           |          |         |Shingle.
+  6  |14 years|Negligible|Ditto      |          |(?)      |Sand.
+  ---+--------+----------+-----------+----------+---------+----------
+
+The least rate of softening noticed, apart from those structures of a
+more recent date, in two of which it was very slight, occurred in a
+pier thirty-eight years old (No. 4), where, of three piles tested, two
+were quite hard, and the third softened 1/10 inch only.
+
+Whatever may be the precise cause of the change, it does not appear to
+be affected by the period or percentage of immersion during the rise and
+fall of tides.
+
+[Illustration: FIG. 59.]
+
+This will be clear from the diagram, Fig. 59, which refers to four piles
+(No. 3 of table), all of the same age, in the same structure. On each
+pile the depth of softening is given at points in strict relation to
+each other, and to the tidal range. The percentages of immersion for the
+various heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening; this,
+indeed, is always greatest near the ground, at whatever actual height it
+may be. For instance, pile A was at ground-level softened 1/4 inch,
+that point being 60 per cent. of its life under water; but on pile B, at
+a point 74 per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level of
+this pile, the percentage being there 87, the softening was no greater
+than at ground-level at pile A.
+
+It is probable that while the percentage of submersion in moving water
+hardly appears to affect the result, yet prolonged contact with wet
+sand, sea-weed, or clinging shell-fish may do so. This seems to suggest
+that the process of change, as between the sea-water and the iron, is
+slow, and to be effective must be continuous; so that it is only found
+to any considerable extent where the water in contact with the surface
+is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1
+foot and 6 inches above ground-level, the surface was in one pile
+shrouded in a thick mantle of heavy sea-weed, and in the other covered
+by molluscs; in both instances the surfaces being thus kept moist and
+undisturbed. The piles of the fourth case were in hard rock, were clean,
+and, where accessible, always either in moving water or quite dry.
+
+However this may be, the power to resist softening certainly appears to
+vary largely with the quality of the iron. The piles, referred to above,
+in which deterioration proceeded at the most rapid rate were certainly
+of a soft metal, the first being markedly so. On the other hand, certain
+piles (No. 4) of hard, close-grained iron suffered very little.
+
+It may be mentioned with respect to the last named, as a matter of
+interest, that the caps of the lower lengths (just above ground-level)
+had been cast with short pieces of wrought iron projecting--possibly for
+lifting purposes--which during thirty-eight years had altered in
+character to something very like softened cast iron, but laminated, and
+harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained
+having the semblance of wrought iron. The percentage of submersion was
+about 60.
+
+A number of piles, not included in the table, varying from fifteen to
+forty-four years old, and of the same structure to which set No. 2
+belonged, were all found to be hard, with the exception of one showing
+3/16 inch of softening. These are omitted, because the mud surrounding
+them was at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points testing might
+have disclosed different results. It is probable that for any piles
+standing in soft material examination below the surface would reveal
+more pronounced softening than where occasionally exposed.
+
+To meet the effects of sea-water on cast-iron piles, and for other
+reasons, it is a common and good practice to make the lower lengths of
+greater thickness--say, 3/8 inch more--than that sufficient for the
+upper. Occasionally, also, the bottom lengths are filled with concrete,
+which no doubt adds to the length of time during which they may be
+relied upon.
+
+
+
+
+CHAPTER X.
+
+EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+
+In the preceding chapters defects of various kinds to which riveted
+bridgework is liable have been more particularly dealt with; it is now
+proposed to consider the examination of such structures, following this
+by a reference to methods of repair and strengthening, leaving the
+treatment of other classes of bridgework to be developed under their
+proper headings, though some of the remarks immediately following will
+apply to all.
+
+The exhaustive survey of a bridge is only to be made after considerable
+experience in the work, but it may be stated that in looking for defects
+it is well to seek where they are least expected, till, with practice,
+one knows better where to direct attention. When examining with a view
+to pronouncing an opinion upon the fitness of the structure to remain in
+place, if in any real doubt, it is wise to give a casting vote against
+it; and finally it may be said that upon taking down a bridge condemned
+for any one or more defects, it should be examined for worse. This may
+seem to be somewhat pessimistic, but is based upon the teachings of
+experience.
+
+Preliminary examination of a bridge may reveal such faults or weaknesses
+as at once to ensure its condemnation; but if this is not the case, and
+there is a reasonable probability that the structure may be given a
+fresh lease of life, it will, for the purpose of estimating the
+strength, or for possible repairs, commonly be desirable to secure
+precise particulars of the existing structure independently of any
+drawings that may be in existence, and which will very probably be
+incorrect, the finished work, if old, seldom agreeing with the contract
+drawings. A final decision may in this case be deferred till after the
+measuring up has been completed, the condition of the structure becoming
+more familiar in the process.
+
+It is desirable first to ascertain whether the bridge remains in good
+form, whether the camber of girders appears to be what might be
+expected, or agreeable with existing records, though much reliance must
+not be placed upon figured cambers, it being quite common for girders to
+leave the bridge yards with the camber something other than that
+intended. The deflections under live load will also be observed, and
+compared with the calculated result, or checked by judgment. The
+calculations upon which strength and deflections are based will, of
+course, refer to the actual sections, which are sometimes a little
+difficult to ascertain if there has been irregular rusting. In
+continuous girders also, levels having been taken, allowance should be
+made for effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the like object. It
+is seldom that the main flanges of girders show signs of weakness,
+unless from flexure in the case of long and narrow top members,
+insufficiently stiffened; but there may be want of truth from other
+causes already dealt with. In plate girders the webs should be most
+carefully scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange angles, if the
+floor rest upon the flange. All riveted connections, of course, need
+close attention, both for straining effects, where there is a liability
+to wracking, and to detect loose rivets. Loose rivets and want of
+tightness in other parts of the work may frequently be detected at
+sight by a reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects of weather;
+it may be seen round rivet-heads or along the edges of angle-bars, or
+other parts where there is movement. Loose rivets, though generally to
+be detected also by the hammer, may perhaps in the case of thin-webbed
+cross-girders be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may sometimes be
+detected by simultaneous deflection tests--with rods--at the top and
+bottom flanges of a girder, at the same distance from the bearings. Any
+difference in the readings may indicate loose web-rivets, or possibly a
+tear in the web running parallel to the flange angles.
+
+Bracings between girders are very apt to display a rich harvest of
+working rivets. Cross-girders and longitudinals also may have loose
+rivets at their connections, and be very badly wasted, with quite
+possibly cracks in the webs, or other defects already enlarged upon.
+
+The condition of the road upon the bridge will frequently be an
+indication of the state of the floor which carries it; or the existence
+of rail-joints which are working badly may very properly lead to a
+critical examination of the girder-work immediately below, as this is a
+fruitful source of damage in light constructions. Floor-plates, where
+these exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the latter
+being often loose and unsatisfactory.
+
+Trough floors may be expected to show loose rivets near the ends, with a
+probability of excessive leakage where they abut against the webs of
+supporting girders.
+
+Floor plates resting upon abutments or piers, being very liable to
+serious decay, require attention, and girder-work entering masonry
+should receive close scrutiny, any obstruction to a sufficient
+examination being removed so far as is judged sufficient for the
+purpose. The structure should, of course, be closely watched during the
+passage of live load for any signs of abnormal movement, excessive
+vibration, or lurching.
+
+In addition to seeking for these various defects, or others which have
+been referred to in these pages at length, it will be well always to be
+alive to the possibility of faults to be seen for the first time, or of
+which the author has furnished no instance.
+
+Having formed a reliable opinion as to the state of the bridge, this, if
+satisfactory, may leave to be determined only the question of strength
+relative to the loads carried. It is apparent that stress limits
+suitable for a new structure, which has all its life before it, of
+purpose moderate to cover possible deteriorations, the growth of loads,
+and other adverse influences, may to avoid immediate reconstruction,
+reasonably be permitted of a higher value for a further term of years in
+the case of a structure which it is known has for a considerable period
+behaved well, and remains in good condition. What this higher value may
+be will be greatly influenced by the circumstances of each case, and,
+being largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the nominal unit
+stress in an old bridge may be a very considerable amount in excess of
+that allowed for new work, without, of necessity, showing any ill
+effects; and the author is of opinion that for old bridges in good
+condition it is quite prudent to allow an excess of 33 per cent. beyond
+that permissible for a new design. If the structure is too weak to
+satisfy this modified condition, it may be possible to bring it within
+the stress limit by a reduction of ballast or other removable dead
+weight. If this expedient does not promise to be satisfactory, or the
+bridge shows actual signs of weakness, or palpable defects, it will be
+necessary to deal with the question of repair, strengthening, or
+reconstruction.
+
+The repair of built up bridgework resolves itself largely into a matter
+of replacing loose rivets by cutting these out, rhymering the holes, if
+desirable, and again riveting. It will often be sufficient to do this
+with no particular precautions as to bolting up temporarily; the rivets
+having been loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to remove all
+the rivets, bolting up securely as this is done, in order to make a
+tight job, taking out each bolt in turn as required, and again filling
+the holes; or it may be well in a bad case first to remove all loose
+rivets, substituting good bolts, in order that work which has gone out
+of shape owing to defective rivets may first be brought true.
+
+Cross-girder webs, cracked vertically or nearly so, are commonly
+repaired with splice-plates on either side; but in doing this it is
+undesirable to add plates of excessive thickness relative to the
+web--probably poor--as by an abrupt change of web section it appears not
+unlikely a fresh break may be favoured.
+
+[Illustration: FIG. 60.]
+
+[Illustration: FIG. 61.]
+
+[Illustration: FIG. 62.]
+
+[Illustration: FIG. 63.]
+
+Replacing wasted flange-plates, or adding new plates to those which
+exist, is occasionally resorted to in the case of main girders, the
+flanges of which are sufficiently accessible, but the operation is
+difficult, takes some little time, and should only be attempted under
+the constant supervision of a thoroughly capable man. When done, if the
+girder has not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the new section,
+the old always taking more by the amount of the dead-load stress
+previously carried. The method which the author has seen applied to
+lattice girders of about 80 feet span, having good angle-bars in the
+flanges, with a shallow vertical web for attachment of diagonals,
+consisted in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been removed.
+The new plate length having been prepared, was, on a Sunday, during a
+few hours’ cessation of traffic, marked off, the temporary bolts being
+removed for the purpose, and then replaced. After the plate had been
+drilled, on a later Sunday, it was finally put into position, bolted up,
+and riveted at leisure; cover-plates make additional trouble, but are
+dealt with on the same principle. The method as shown in Fig. 60 is,
+however, barely practicable for so many plates. It is preferable, if it
+is proposed to add section, to do this with as little interference as
+possible with existing rivets of importance. This may be accomplished,
+if the existing plates are not too wasted at their edges, by riveting on
+new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength
+of a girder is increased by the addition to the top or bottom boom of
+material in such a form as sensibly to increase the depth, and thus,
+while adding increased section to one boom, to reduce the stress in
+each, though to dissimilar amounts. By this device also the relief is
+effective only as regards the live-load stress; under dead load only the
+new material does no work, provided, of course, that no relief staging
+was used during the alterations. For girders carrying any considerable
+proportion of dead load the method is very inefficient, though for
+others, in which the live load is relatively large, the result should be
+more satisfactory.
+
+As this question of adding new section to old is of much importance in
+dealing with repairs and strengthening operations, a few general remarks
+upon the subject will be pertinent. The difficulty in such work commonly
+is to cause the new to render any considerable assistance to the old in
+those cases which occur in practice. If a bar be imagined under
+longitudinal stress varying between 0 and a maximum, then, if the area
+of the piece be increased at the time when it takes no stress, its
+capacity for resisting the maximum amount will be increased, and for
+added material of similar elasticity the unit stress proportionately
+reduced. If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any degree.
+To take a third case, of the maximum being twice the minimum load, it
+will be necessary, in order to lower the maximum unit stress by 25 per
+cent., to double the original section of the bar if, as supposed, the
+extra metal has been added to the piece when under the smaller load, so
+that the new section is only effective in assisting to carry the
+remainder of the load at such times as it may be imposed. The
+relationship stands thus:--
+
+      Live load         New area
+  ---------------- × -------------- = relief.
+  Live + dead load   New + old area
+
+These statements will be true under the conditions named, within the
+elastic limit of the material; but some advantage would be derived in
+the second case, and a more marked benefit in the third, if the load
+assumed to be a maximum were exceeded, or if the composite bar were
+tested to destruction; as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment as to how
+far this reserve of strength may be considered of value.
+
+If, instead of simply adding section to the bar, some part of the
+constant load is put upon the new section by the manner of attachment,
+the combination will, of course, be more effective.
+
+To apply these considerations and illustrate the way in which the two
+methods of adding flange section work out when reduced to figures, the
+case will be supposed of a girder 6 feet deep, carrying a load of which
+one-third is dead and two-thirds live. To the flanges of this girder are
+added plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the girder before
+strengthening is liable, the depth remaining substantially unaltered.
+With dead load only the original section would be stressed to 2·3 tons
+per square inch, the new section being then unstressed. Under full load
+the new and old material take 3·1 tons per square inch additional,
+making the modified stress on the original section 5·4 tons per square
+inch, as against 7 tons; or a reduction of 22 per cent. This compares
+with 33 per cent., the relief due to 50 per cent. increase of flange
+area under ordinary conditions of stress distribution.
+
+Let the second method of strengthening the girder now be considered,
+using, for purposes of comparison, the same total amount of new material
+to increase the girder depth by an addition to the top flange. This
+section will be equal to the area of one flange, which, though it may
+be applied in many different ways, giving a greater or a less increase
+to the depth, would probably be used in some such manner as that shown
+in Fig. 64, increasing the effective depth for live-load stress by
+nearly 10 inches.
+
+[Illustration: FIG. 64.]
+
+The added material will, as in the previous case, leave the dead-load
+stress unaltered, or 2·3 tons per square inch. The stress in the bottom
+flange due to live load will, however, now be 4·1 tons per square inch,
+making a total stress of 6·4 tons per square inch, against 7 tons--the
+original stress. The reduction here is 8 per cent. only, as compared
+with 12 per cent., the relief due, under ordinary conditions, to an
+increase of effective depth from 6 feet to 6 feet 10 inches, and by the
+use of additional material, equal, as before, to one-half of the total
+flange areas before the alteration.
+
+The effect on the top flange need not be here gone into in detail, but
+it may be said that, owing to the increase of gross section and of
+depth, the ultimate stresses of both the new and old material are
+greatly less than as given for the bottom flange.
+
+Girders strengthened by the first of these two methods would, it is
+probable, if tested to destruction, give results more nearly in accord
+with the actual percentage increase of flange section, plastic
+deformation of the metal, before failure, tending to reduce the
+differences of stress on the new and old material of the sections.
+
+[Illustration: FIGS. 65 and 66.]
+
+Web members of lattice girders may, if weak, sometimes be dealt with by
+the introduction of supplementary bars, parallel to and between the old
+members, or by the addition of strips or angles to the existing
+diagonals. The treatment will be largely influenced by the nature of the
+old detail, which may lend itself to some one arrangement much better
+than to any other.
+
+End riveting of web members may, if it has become loose, be dealt with
+by simply rhymering the holes a size larger, and re-riveting in the best
+manner, if the stresses are not excessive; or it may be necessary to
+devise some additional attachments by which new rivets are brought into
+use (see Figs. 65 and 66). The effective relief due to supplementary
+rivets will be influenced by similar considerations to those governing
+increase of section.
+
+[Illustration: FIG. 67.]
+
+[Illustration: FIG. 68.]
+
+Old structures are very frequently deficient in bracing, which may, in
+such cases, be advantageously introduced; or girders individually weak
+may be rendered collectively efficient by suitable bracing. In
+considering the advisability of this, however, the case should be viewed
+with regard to the possible effects of such members, as already dealt
+with in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders may have
+the effect, under live load, of increasing the stress on the outer
+girders due to twisting of the structure as a whole, though the inner
+girders will, except for full loading of the whole bridge, be advantaged
+as to stress values, and in any event bettered by being held up to their
+work. The effect upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations the
+detail should be schemed with special care to ensure simplicity in
+execution, smith’s work being rigorously avoided. A good arrangement for
+supplementary bracing between plate-girders, which gives little trouble
+in carrying out, is shown in Fig. 67; or where the stiffeners of such
+girders are in line across the bridge, the detail given in Fig. 68 may
+involve less expenditure. Difficulties may be experienced in riveting,
+unless great care is taken in the positioning of rivets. Fitting-bolts
+are only to be relied upon as such, if they really justify the name;
+they are, though easy to specify, by no means easy to secure under the
+conditions of practical work. Weak cross-girders may make
+alterations--in some cases considerable--necessary, to rectify the
+defect of strength. The removal of old girders to make room for new is
+seldom resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders between the
+old in cases where there is no plated floor to make the work difficult.
+By this method there is, of course, an increase of appreciable amount in
+the dead load carried by the main girders, which would in many instances
+be objectionable. With deep and heavy main girders, having plate webs,
+cross-girders may be strengthened by improving the end connections by
+suitable gussets, and attachment to good vertical stiffeners, the fixity
+of the ends thus aimed at being assured by overhead struts or girders,
+from one main girder to its fellow, at intervals apart well considered
+with reference to the horizontal strength of the top flanges, the whole
+thus making a closed frame, as shown in Fig. 69. The method appears
+feasible, but it should be stated that the author has not known it to be
+applied in its entirety as a means of strengthening an old floor.
+
+[Illustration: FIG. 69.]
+
+A simple and very common device consists in substituting for the
+ordinary cross-sleeper road, where this exists, stout timber
+longitudinals under the rails, which have, where the cross-girders do
+not exceed 5 feet centres, a marked distributive effect, tending to
+reduce the maximum load upon any individual girder. With a similar
+object, trough girders containing longitudinal timbers are sometimes
+adopted where the depth available is not enough to enable sufficiently
+stiff timbers to be used alone. In either case the object sought is the
+same--to modify the effect of the heavier wheel loads upon isolated
+cross-girders. When the spacing is so close as 4 feet, the beneficial
+result of this treatment is considerable, but at 8 feet centres it can
+have but a moderate effect where timbers alone are used.
+
+Occasionally, for long cross-girders, a distributing girder is placed,
+with the same intent, in the 6 feet way, its function being limited to
+this use only if the depth and strength are sufficiently small to serve
+this object alone, as distinct from the case in which it becomes a
+carrying girder transferring load to the abutments. As a distributor
+simply, the girder has to equalise the bending moments amongst the
+cross-girders, to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous to
+alteration, for a position of the wheel loads such that the heaviest
+comes upon a centre cross-girder, the mean of these moments will, when
+compared with that for each girder, show the difference to be induced as
+a result of introducing the distributor. These differences of moment
+render necessary at the centre of the cross-girders reactions upwards or
+downwards, as the case may be, of amounts competent to induce moments
+below the inner rails equal to these differences.
+
+It is these reactions which must be provided by the distributing girder
+at a moderate stress, and without flexure of such an amount as sensibly
+to modify the reactions. The greatest section necessary at any one point
+may then be adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no harm in a little
+excess in a case of this kind, the total cost being but little affected
+by some small addition to the weight, where labour upon the site is so
+considerable an item as in work of this description. The ends of the
+distributing girder should be carried on to the abutments or piers to
+ensure adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at an early
+stage, by boning or by levelling, the condition of the cross-girders as
+to uniformity of heights, as this may affect the length most suitable
+for separate sections. Between the underside of the distributor and the
+cross-girder tops there will commonly be spaces of varying amounts,
+which should be filled by packings to fit, rather than by pulling the
+work together by force, introducing undesirable stresses of uncertain
+amount.
+
+In the earlier remarks upon the strengthening of bridgework by the use
+of new material, it has been assumed that the modulus of elasticity of
+the new metal is similar to that of the old; it may, however, as in
+cases where wrought-iron work is reinforced by additions in steel, be
+necessary to take the difference of elastic properties into account,
+with which object the new section should be multiplied by a quantity
+(greater or less than unity) inversely proportional to the higher or
+lower modulus of the new material, that is to say, by
+
+  E of old material
+  -----------------
+  E of new material
+
+
+
+
+CHAPTER XI.
+
+STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+
+The addition of distributing girders, described in the last chapter, as
+a means of strengthening a bridge floor, while sufficient in many cases
+so far as the cross-girders are concerned, does not in any appreciable
+way assist the main girders. When for a two-line bridge, having outer
+main girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders may be used,
+placed either above or below the cross-girders, on the centre line of
+the bridge.
+
+There are two principal ways in which such a girder may be brought into
+use; the easier, but generally less economical, is by making a simple
+attachment to the cross-girders, the old girder work still taking the
+whole dead load. By this method the new girder does no work but carry
+itself till the live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the second
+method is to make the connection adjustable, so that a part of the floor
+weights may be imposed upon the new girder as an initial load. In doing
+this the old outer girders will rise slightly, being relieved of stress,
+and the cross-girders also lifted at the middle, whilst the new girder
+is depressed as the load is brought upon it. With some part of the live
+load a very considerable proportion of the total may in this way be
+carried by a centre girder of moderate section. The whole question, by
+either method, turns upon deflections; and it is in determining the
+relative movements of the girders that the problem chiefly lies.
+
+It is convenient first to determine the percentage of load relief to be
+effected in the main girders, as to which it is to be observed that as
+this relief (distributed) is induced by the upward reaction of the new
+girder acting at the centre of the cross-girders, the stress relief of
+these will, as a rule, greatly exceed that of the outside girders. For
+the generality of cases, it may be taken that the relief suitable for
+the outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress in these
+to a greater degree.
+
+If, however, it be thought desirable to check this, it may be done by
+considering a cross-girder subject to its dead and live loads acting
+downwards, and to reactions at the centre and ends. At the centre the
+reaction will be the load of which the two main girders are relieved on
+a length equal to the pitch of the cross-girders, or as here given:--
+
+  _c_ × _t_ × P = reaction at centre (1)
+
+_c_ being the percentage of relief; _t_ the total load per foot run of
+the bridge; and P the pitch of cross-girders. The live loads carried by
+the cross-girders are for this purpose taken at per foot run, as for the
+main girders. With these data it will be easy to construct a diagram of
+moments, making it evident whether the relief proposed for the main
+girders will give a sufficient percentage of relief to the floor beams.
+
+Granting that this proportion has been decided, and dealing first with
+the case in which the centre girder is simply attached to the
+cross-girders, and takes no dead load other than its own weight, then
+the live load carried by the outside girders, and previously borne
+wholly by them, will be reduced by the amount it is intended to transfer
+to the centre girder, and will become
+
+  L{_l_} - (_c_ × L{_t_}) = live load on outer girders (2)
+
+L{_l_} being the total live load, and L{_t_} the total dead and live
+load carried by the bridge. From this the deflection of the outer
+girders corresponding to this modified live load may be derived.
+
+[Illustration: FIG. 70.]
+
+It is next necessary to ascertain the vertical movement, commonly a
+depression, of the cross-girders at the centre relative to their ends,
+when subject to the running load only, and supported at the middle and
+ends, the centre reaction being obtained as before indicated (1). This
+movement will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the upward
+flexure of the girder due to the centre reaction, considered as separate
+effects. Stress values having been estimated for the two conditions,
+these results may readily be deduced by simple flexure formulæ,
+observing that while the curve of moments due to live load sufficiently
+approximates to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter “Deflections,”
+the flexure due to the centre reaction will be but 0·80 of that which
+corresponds to the same stress for distributed loading. Or, the curve
+assumed by the girder under live load may be plotted by a method to be
+later explained.
+
+The sum of the movements now determined--that is, the live-load
+deflection of the outer girders, and depression, as is commonly the
+case, of the cross-girders--will give the extreme depression (marked _m_
+in Fig. 70), from the dead-load condition of the middle cross-girders,
+when supported to the extent desired by a centre girder whose
+proportions are not yet known, but which, carrying the required
+percentage of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the flanges of the
+new girder, governed by this flexure, will for a plate girder be
+
+  D × C × _m_
+  ----------- = _f_, unit stress on gross section (3)
+     S^{2}
+
+D and S being, as before (see “Deflections”), the depth and span
+respectively in feet, C a constant, _m_ the deflection in inches, and
+_f_ the stress per square inch on the gross section of flange.
+
+The gross area A, of the flange, is given by
+
+  S × _c_ × L{_t_}
+  ---------------- = gross area of flange (4)
+    8 × D × _f_
+
+_c_ × L{_t_}, being, as in (2), the load transferred to and carried by
+the centre girder.
+
+The actual stress in the flanges will, of course, be greater by an
+amount due to the girder’s own weight; but this does not affect the
+question of relief. For any ordinary case the stress per square inch
+will be low; but it will manifestly be useless to assume a greater
+stress with a view to economy, as the effect of reducing the section
+will simply be to make the girder too flexible, thus causing it to be
+less effective than primarily intended. If, as is seldom the case, there
+is freedom as to the depth of girder permissible, it is evident the unit
+stress may be made a condition, and the depth deduced by a suitable
+modification of formula (3); the relief desired being in this way
+equally well assured. Indeed, in the rare instances in which any depth
+may be adopted, this method is--contrary to the general rule--distinctly
+economical, particularly if the girder may be placed below the
+cross-girders, which simply rest upon it, without elaborate attachments.
+
+[Illustration: FIG. 71.]
+
+Considering now the second method of applying centre girders by which
+the new girder is made initially to carry part of the dead load, by
+adjustment, it will at once be recognised as a more complex matter. The
+measure of relief by which the old girderwork shall benefit need not be
+affected by the method of applying the centre girder, and may be decided
+on the principles already considered. The outer girders carrying a
+reduced load, when the bridge is fully loaded, and the cross-girders
+being in part supported at their centres in the manner already
+described, will give a resulting depression _m_ (see Fig. 71) of the
+centre cross-girders, below the original dead-load position, of a
+similar amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre girder, which may
+be designed to carry the required percentage of the total bridge loads
+with the maximum stress and depth, as conditions, leaving the initial
+dead load and necessary adjustments to be ascertained. This is the
+common case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.
+
+The centre girder of fixed depth being then required to carry a definite
+load at a definite flange stress, will deflect a definite amount at this
+stress. If this deflection equalled the extreme depression _m_ of the
+old girder work, no adjustment would be necessary, the centre girder
+then carrying no initial dead load, as by the first method; but for
+centre girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally being small,
+and in order to ensure that the new girder shall do its full work, some
+dead load must be put upon it. In the act of adjustment the
+cross-girders must be lifted and the centre girder depressed, till the
+joint movement equals the excess _s_ of the centre girder deflection
+over _m_, when the new girder will carry the proper amount of initial
+load, and upon further deflection under live load give the full measure
+of relief. The amount of “lift” or upward flexure of the old girder
+work, and the depression or “drop” of the new girder, during adjustment,
+will depend upon relative stiffness, and may be ascertained as
+follows:--
+
+For unit reactions at the centre of the cross-girders the upward flexure
+of these may be ascertained, as also the upward flexure of the two outer
+girders when subject to forces of the same total amount (one-half to
+each) applied at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are subject to
+unit lifting forces; similarly, the depression of the centre girder for
+unit loads applied at the cross-girders may be determined. There will
+then be known the movements upwards and downwards of the old and new
+work when being drawn together by unit forces applied as stated.
+
+If
+
+  _l_    = lift due to unit loads,
+  _l{t}_ = total lift due to adjustment,
+  _d_    = drop due to unit loads,
+  _d{t}_ = total drop due to adjustment,
+  _s_    = deflection excess = gross adjustment,
+
+there will then be
+
+     _d_
+  --------- × _s_ = _d{t}_,
+  _l_ + _d_
+
+total drop of centre girder under adjustment,
+
+     _l_
+  --------- × _s_ = _l{t}_,
+  _l_ + _d_
+
+total lift of centre cross girders under adjustment,
+
+  _d{t}_
+  ------ × unit load =
+   _d_
+
+initial load put upon centre girder at each cross-girder.
+
+The rise of the two outer girders for upward forces together equal to
+those depressing the centre girder may readily be deduced.
+
+[Illustration: FIG. 72.]
+
+[Illustration: FIG. 73.]
+
+The act of adjustment may conveniently be effected by the arrangement
+shown in Fig. 72, in which each cross-girder is hung up at its centre by
+four bolts. At the middle of the centre girder the total amount to be
+screwed up will be that corresponding to the deflection excess _s_, but
+towards the ends this amount decreases, and may advantageously be
+represented by a diagram as Fig. 73, in which, if _s_ represents to
+scale the amount to be screwed up at a centre cross-girder, the
+corresponding amounts for other girders may be read off direct. It will
+be apparent that it must be necessary to place the centre girder at
+such a height as to leave a space between the old and the new work
+greater than the amount to be screwed up, this excess clearance being
+ultimately filled by a packing.
+
+The precautions to be observed in carrying out this kind of work, and
+the practical methods of adjustment adopted by the author after some
+little experience, may here be given.
+
+Great care is necessary at the outset to ascertain the true spacing of
+the cross-girders, to ensure that the bolt-holes in the bottom flange of
+the centre girder shall come where desired. The fixing of the
+cross-girder brackets also needs close attention to avoid after trouble,
+the bolt-holes in the brackets being preferably drilled on the site
+after fixing. It will, for masonry abutments, be necessary to fix
+bedstones to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps leave the
+stones liable to settle slightly when the full load is carried. To
+eliminate the bad effect of this upon the ultimate adjustment, and to
+take up any initial set of the new girder work, which would be
+prejudicial in the same way, it is desirable, the centre girder being in
+place, to screw up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it is
+convenient to prepare, for use at the bridge, a diagram somewhat similar
+to Fig. 73, giving the amount by which the new and old work are to be
+brought together at each cross-girder, with the number of turns for each
+nut to effect this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is repeated as
+often as necessary, and so managed as to bring all up proportionately to
+the final requirement, keeping tally with chalk marks over each
+cross-girder as a check. The preliminary screwing up should be conducted
+with little less care than that adopted for the later adjustment, to
+avoid damage to the old work. This later adjustment having in due course
+been effected, it is then necessary to measure for packings to fill the
+spaces remaining between the old cross-girders and the new centre
+girder. These spaces should be callipered at each of the four corners,
+care being taken to avoid after-confusion. The measurements ascertained
+will, however, be too great for the finished packings, as an allowance
+of not less than 1/10 inch (total), will commonly be wanted to cover
+irregularities in the surfaces. The packings, having been prepared and
+checked, may be slipped into place after slacking all the bolts a small
+amount to permit this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last operation.
+
+As a check upon the calculations and adjustment, the “lift” of the outer
+girders and cross-girders, and the “drop” of the centre girder may be
+observed by levelling. For this purpose the author has used a staff of
+inches divided into tenths, with which, and a good level, very accurate
+readings may be taken for short distances.
+
+No reference has been made to the effect of skew in a bridge on the
+above methods, the explanation given applying rather to bridges square
+on plan. The influence of skew on the load distribution will largely be
+a matter of detailed calculation. The flexure of the girders may also be
+sensibly affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to modify the
+amount of screwing up during adjustment, which may be better understood
+by reference to Fig. 74, and comparing it with Fig. 73, the adjustment
+diagram for a square bridge.
+
+To illustrate how these methods of strengthening work out, and compare
+as to weights of centre girders required, the case has been assumed of a
+wrought iron bridge of 60-feet span, having outer girders 5 feet deep,
+of 39 square inches gross flange area; and cross-girders, at 8-feet
+centres, 27-feet span, 1 foot 9 inches deep, with a gross flange area of
+twenty square inches. The dead load and live load on either road are
+each 1·75 tons per foot run.
+
+The stress in the outer girders previous to the alteration being 6 tons
+per square inch gross, it is desired to relieve this to the extent of 33
+per cent. by a steel centre girder. In the table here given the
+quantities given in italics are fixed as primary conditions:--
+
+CENTRE STRENGTHENING GIRDERS FOR 60-FT. SPAN.
+
+  ----------------------------+-----------+------------+------------
+                              |  Centre   |  Centre    |
+                              |  Girder,  |  Girder,   |Adjustments
+             ----             |  Stress   |   Depth    | Unknown.
+                              |  Unknown. |  Unknown.  |
+  ----------------------------+-----------+------------+------------
+       _Outer Girder._        |           |            |
+                              |           |            |
+  Deflection under modified   |           |            |
+  live load                   |  ·42 in.  |  ·42 in.   | ·42  in.
+  Lift of adjustment          |   _nil_   |   _nil_    | ·153  „
+                              |           |            |
+      _Cross Girders._        |           |            |
+                              |           |            |
+  Depression under live load  |           |            |
+  --modified conditions of    |           |            |
+  support                     |  ·13 in.  |  ·13 in.   | ·13   „
+  Extreme depression (_m_)    |  ·55  „   |  ·55  „    | ·55   „
+  Lift of adjustment (cross-  |           |            |
+  girder only)                |   _nil_   |   _nil_    | ·095  „
+  Total lift of adjustment    |           |            |
+  (_l{t}_)                    |   _nil_   |   _nil_    | ·248  „
+                              |           |            |
+      _Centre Girder._        |           |            |
+                              |           |            |
+  Depth                       | _3·5 ft._ |  8·2 ft.   |_3·5 ft._
+  Unit stress on gross section|           |            |
+  (ex girder’s weight)        | 2·14 tons | _5·0 tons_ |_5·0 tons_
+  Total deflection (ex        |           |            |
+  girder’s weight)            |  ·55 in.  |  ·55 in.   |1·28 in.
+  Deflection excess (_s_)     |   _nil_   |   _nil_    | ·73  „
+  Depression, or “drop” of    |           |            |
+  adjustment (_d{t}_)         |   _nil_   |   _nil_    | ·482 „
+  Gross area of flange        |105 sq. in.|19·2 sq. in.|44·5 sq. in.
+  Weight                      |  20 tons  |  10·4 tons |11·4 tons
+  Net flange stress (including|           |            |
+  girder’s weight)            | 3·19 tons |  6·87 tons | 6·94 tons
+  ----------------------------+-----------+------------+------------
+
+Girders subject to distributed load are treated as having uniform
+stress, but where this is not strictly the case, as in some light
+girders, it will be necessary to take the fact into account. For centre
+girders of wrought iron, and a unit stress on the gross section of 4
+instead of 5 tons, the girder weights are between 9 and 10 per cent.
+greater.
+
+[Illustration: FIG. 74.]
+
+In the above treatment of the application of centre strengthening
+girders there is a source of error which should be touched upon. If,
+under live load, the centre girder deflects more than the outer girders,
+as it commonly will, there must be a want of uniformity in the behaviour
+of the cross-girders, those near the abutments being more relieved than
+the estimated amount of relief of those at the centre, which will have
+less than that intended; but the reduction of stress in the
+cross-girders will generally be so considerable that any such ambiguity
+of excess or defect is commonly unimportant; the effect of this also
+upon the main girders is much less than might be supposed, being, for
+the third of the cases just given, about 2-1/2 per cent. excess for the
+centre girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as approximate only.
+It is possible to eliminate some part of the error by lifting the end
+cross-girders during adjustment, a less amount than that given by the
+diagrams, Figs. 73 and 74, taking care that the centre girder is
+depressed its full amount by lifting the centre cross-girders a little
+more; this refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.
+
+Particulars are here given of five ordinary cases, comparing the
+calculated and observed results of adjustment. The operation of
+levelling was conducted by a quick-eyed and capable assistant, who was
+not made acquainted with the results expected, in order to avoid any
+sub-conscious tendency to match the calculated figures:--
+
+EXAMPLES OF CENTRE GIRDER ADJUSTMENTS.
+
+  ---------------------------------------+-----------+-----------------
+                    --                   |Calculated.|    Observed.
+  ---------------------------------------+-----------+-----------------
+                                         |   in.     |    in.
+                                         |           |
+                          No. 1.--56-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·82     |    ·84
+  Lift of cross-girders at centre        |   ·23     |    ·22
+  Lift of outer girders                  |   ·20     |·10 and ·13
+                                         |           |
+                          No. 2.--57-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·50     |    ·50
+  Lift of cross-girders at centre        |   ·18     |    ·20
+  Lift of outer girders                  |   ·11     |·08 and ·10
+                                         |           |
+                          No. 3.--67-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·70     |    ·75
+  Lift of cross-girders at centre        |   ·15     |    ·17
+  Lift of outer girders                  |   ·10     |    ·09
+                                         |           |
+                          No. 4.--68-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·70     |    ·65
+  Lift of cross-girders at centre        |   ·20     |    ·18
+  Lift of outer girders                  |   ·13     |    ·14
+                                         |           |
+            No. 5.--52-_Ft. and_ 28-_Ft. Spans continuous._
+                                         |           |
+                                         |Long |Short|Long |Short
+                                         |Span.|Span.|Span.|Span.
+  ---------------------------------------+-----+-----+-----+-----------
+                                         | in. | in. | in. | in.
+  Depression of centre girder            | ·28 | ..  | ·29 | ..
+  Lift of centre girder                  | ..  | ·04 | ..  | ·03
+  Lift of cross-girders (centre of spans)| ·17 | ·09 | ·15 | ·13
+  Lift of outer girders                  | ·08 | ..  | ·08 | ..
+  Depression of outer girder             | ..  | ·01 | ..  |negligible.
+  ---------------------------------------+-----+-----+-----+-----------
+
+The method of calculation adopted for these cases was not precisely that
+given, though depending upon the same broad principles. The first cannot
+be considered a good example. The last, having continuous girders, of
+course needed special treatment.
+
+Of about seventeen bridges strengthened in the manner described, the
+effect generally was satisfactory, in reducing deflection and vibration;
+but in two cases of small span, owing probably to settlement of
+bedstones, the results were not so good.
+
+From first to last the work of putting in a centre girder takes some
+little time, owing to the slow progress generally made in fixing the
+brackets, preparing packings, etc. The cost of a typical case was about
+23 per cent. of the cost of a new superstructure, with a 30 per cent.
+relief of stress.
+
+[Illustration: FIG. 75.]
+
+[Illustration: FIG. 76.]
+
+A special case of strengthening by a centre girder, having considerable
+interest, may be here referred to. The primary idea involved was not the
+author’s. The bridge dealt with has already been noticed under “Bracing”
+and a section, before alteration, shown in Fig. 26. The span being 85
+feet, there was no room for a centre girder of sufficient depth above
+the cross-girders and between the roads, nor was it considered
+economical to place the girder wholly below the floor, because of the
+costly staging this would have necessitated for erection purposes, the
+height above ground level being very great. A girder was therefore
+designed, having open latticing at an angle of 60 degrees, with a bottom
+boom to be below the cross-girders, the top being as high above the
+rails as could be permitted (see Figs. 75 and 76). A temporary boom was
+arranged at the intersection of diagonals, the lower boom proper not
+being fixed till the girder having been lifted into place, with the
+diagonal members passing between the cross-girders, allowed this to be
+done. The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being then 2 inches.
+The permanent boom was then put in place, and the girder restored as
+nearly as was practicable to the camber it was intended to have when
+complete, but without throwing, during the process, any improper loads
+upon the old work.
+
+The lower boom being finally riveted up, the cross-girders were made to
+bear upon it by suitable packings. There were, in addition to the new
+girder, two stiff frames between the old main girders, to which the new
+was secured.
+
+The girder was designed with the intention that under dead load only the
+cross-girders should just rest, but throw no weight, upon the new work,
+the latter assisting to carry live load only. The floor beams being of
+small span, and securely riveted to the old girder tops, the centre
+girder was required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion, the three
+points of support of the cross-girders thus not altering their relative
+levels. That this resulted was evident from the fact that, previous to
+connecting the cross-frames to the centre-girder, the work being
+otherwise complete, a space between the two of about 1/2 inch,
+afterwards filled by a packing, showed no alteration, the closest
+measurement failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be expected, very
+marked.
+
+In the conduct of that class of strengthening work which has been dealt
+with in this chapter, it is essential, in the author’s judgment, that
+the man responsible for the detailed calculations and design should
+himself see the operations of adjustment carried out, or delegate it
+only to one equally familiar with the requirements.
+
+Before dismissing the subject, it will be well to refer to a method of
+approximately determining flexure curves, of occasional use in dealing
+with centre girder or similar questions. The figure assumed is plotted
+to an exaggerated scale, with which object the actual radius of
+curvature at points along the girder’s length are first ascertained by
+the formula
+
+   E × D
+  ------- = R, radius of curvature in feet,
+  _f_ × 2
+
+and the radius of curvature for the diagram by
+
+  12 × R × F^2 = _r_, radius for plotting, in inches (5)
+
+E being the modulus of elasticity, D the girder’s depth in feet, _f_ the
+mean of the extreme flange stresses per square inch of gross area, and F
+the fraction indicating scale as 1/48, where 1/4 inch = 1 foot. The
+curve, being plotted, shows by direct scaling the movement of any point
+relative to its original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn with the help
+of template curves, or even set out as pieces of “straight.”
+
+When the curve is laid down so that its chord equals the span to scale,
+the method involves an error of excess in the resulting deflection or
+droop which is as much as 7 per cent. when the mean radius for plotting
+equals the span as drawn, or when the droop of curve approaches
+one-eighth of the span. As the exaggeration of curvature is made less
+pronounced, this error rapidly diminishes, till for a droop of about
+one-sixteenth the percentage is one-fourth part of that above given.
+This excess in the droop of curve may be amended by the following
+expression:--
+
+          (droop^3       )
+  droop - (------- × 3·73) = corrected droop, or deflection.
+          (chord^2       )
+
+For some purposes it may be preferable to amend the radii for plotting,
+so that the curve, as laid down, shall be correct, which may be
+effected by the formula here given, to be applied to each value of r, as
+first ascertained:--
+
+        (chord^2        )
+  _r_ + (------- × ·0625) = corrected plotting radius.
+        (  _r_          )
+
+If, however, the length of curve is made equal to the span (the chord
+then being less), and the radii for plotting as given by (5) are used,
+the result will for most purposes be sufficiently precise, though there
+will now be an error of a contrary kind, which, for a curve having a
+droop of one-eighth, will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described by
+Professor Fleeming Jenkin in the article “Bridges” of the “Encyclopædia
+Britannica,” but without corrections.
+
+A careful comparison of results by the above means, with those
+calculated, shows that with good draughtsmanship they may be relied upon
+for considerable accuracy. Equally applicable to girders of varying
+depth and flange stress, they have also a limited use in cases of
+continuity.
+
+[Illustration: FIGS. 77 and 78.]
+
+Figs. 77 and 78 illustrate the deflection and stress diagrams for the
+cross-girders of the bridge supposed to have been strengthened by a
+centre-girder, when under the influence of live load and a centre
+reaction of a definite amount. As a matter of convenience, each radius
+length has been halved, before correction, so that the resulting droop
+of the curve is twice the true amount.
+
+
+
+
+CHAPTER XII.
+
+CAST-IRON BRIDGES.
+
+
+Cast Iron as a material for bridges has of late years fallen into
+disrepute. It is now entirely tabooed by the Board of Trade for railway
+under-bridges, unless of arched construction. This condemnation of cast
+iron followed, and was apparently the result of, an accident which
+occurred to an under-bridge on one of the southern lines, which bridge
+had already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good, inasmuch as it
+led to a thorough overhaul of all railway under-bridges in this country,
+and the renewal of a great number no longer in a condition suited to the
+carriage of heavy or of passenger traffic; yet there is little doubt
+that, in the author’s judgment, many excellent cast-iron bridges were
+then removed at considerable cost, to be replaced by others of wrought
+iron or steel, which will not last so long as many of those displaced
+had done, or would still have lasted had they not been dismantled.
+
+The earlier cast-iron bridges were commonly made of cold-blast iron, a
+material of such strength and toughness as to give an extraordinary
+amount of trouble in breaking up the heavier parts, when the time
+arrived to do this, and with which material ordinary hot-blast iron is
+not to be compared for reliability.
+
+[Illustration: FIG. 79.]
+
+As illustrating the very considerable stress to which cast iron may be
+subjected, without of necessity leading to any mishap, two cases may be
+cited. The first, a bridge of 32 feet effective span, carrying two
+lines of way, each pair of rails being supported upon Barlow rails,
+forming the bridge floor, the ends resting upon the bottom flanges of
+inverted [T]-shaped girders, 2 feet 3 inches deep, as shown in Fig. 79.
+
+The extreme fibre stress works out at 2·9 tons per square inch in
+tension, and 5·9 tons per square inch compression, calculated as it
+would be in ordinary office work; but for the actual loads, at a span as
+above, exceeding the clear span by 6 inches only, and without regard to
+the effects of eccentric application of the load. The girders when taken
+out showed upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be too
+strongly condemned, notwithstanding that in this case no ill resulted.
+It is evident that a piece of the lower flange being broken out from
+this cause, as occasionally happens, might so reduce the section as to
+result in complete failure.
+
+[Illustration: FIGS. 80 and 81.]
+
+The second example is that of a small railway under-bridge of two spans,
+continuous over the central pier, each span being 16 feet 6 inches. The
+rails were supported upon longitudinal timbers lying within
+trough-shaped girders, as shown in Figs 80 and 81.
+
+The stress over the pier, in the extreme fibres of the top flange, is
+estimated at 4·7 tons per square inch in tension, but it should be noted
+that the effect of the timber longitudinal and rail has been neglected
+in arriving at this result, which might possibly on this account be
+reduced to near 3 tons per square inch.
+
+The case is noticeable because no evidence of high stress was apparent.
+The author saw nothing to suggest sinking of the central pier, the
+effect of which, within limits, would be to further reduce the stress as
+calculated; but it is quite possible some slight settlement had
+occurred; this, as the spans were so small, would have a sensible
+effect. While too much reliance should not, it is clear, be placed upon
+any estimated result about which there is a lingering doubt, it should
+be remarked that, as it would be necessary the pier should sink 3/16 of
+an inch, for each ton of reduced stress, it is not probable that the
+results quoted are in excess to any material degree; they are, indeed,
+more probably low, as no notice has been taken of impact.
+
+Though cast-iron girders for railway under-bridges are now prohibited in
+this country for new works, there are still uses to which they may be
+applied, and it may be well to insist that girders of this material
+should be fairly loaded, the weight being brought upon them in such a
+way that there shall be no serious secondary stress, such as arises when
+wide flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking down under a
+load fairly applied. Preference is now given to steel or wrought iron
+for columns; while this is often quite justifiable, there remain many
+cases in which nothing better need be desired for this purpose than good
+cast iron, provided only that the column be loaded in a suitable
+manner--i.e., axially, and that the arrangement and details of the
+super-structure are such that there shall be no cross-breaking efforts,
+or rocking of the column due to temperature or other causes; unless,
+indeed, such cross-breaking or rocking is definitely taken into account
+in designing the work. The same care observed in the detailing of
+cast-iron work that is not infrequently taken in the design of
+structures made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with the
+advantage of greater resistance to rust, and a reduced cost in
+maintenance.
+
+Good cast iron is, in fact, when used with discretion, a most excellent
+material, popular predjudice notwithstanding. The oldest metallic bridge
+in this country at the present moment is of that metal.
+
+The one chief respect in which cast iron is at a disadvantage compared
+with wrought iron or steel is that it does not give premonitory warning
+of failure--it remains intact, or it breaks. The indications of
+weakness, which may be read by an experienced inspector of other
+metallic bridges, are in a great measure absent. There is also an
+objection which may exist, but is to be avoided by good design and care
+in the foundry--viz., internal stress due to unequal cooling. In extreme
+cases this may lead to fracture before the work has left the maker’s
+hands, but it can only occur by neglect of ordinary precautions.
+
+[Illustration: FIGS. 82 and 83.]
+
+In a case which has already been referred to in the chapter on
+“Deformations,” page 80, an outer rib of a cast-iron arch fractured near
+the crown after fifty-four years’ use. Owing to the nature of the
+design, and the fact that the near abutment had closed in slightly,
+bringing the linear arch of necessity near the lower edges of the arch
+segment in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces, at the
+upper edge where fracture commenced. The result was very far from
+explaining the occurrence of the break, but an examination of the
+details shown in Figs. 82 and 83 will make it apparent that, in addition
+to the tensile stress, as calculated, there was probably a severe
+initial stress of the same character due to irregular cooling in the
+foundry half a century before. The sum of these stresses, it is
+suggested, placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent either by
+producing a small further settlement of the foundations, of which the
+author saw no evidence, or, as is more probable, the attachment of a
+rope to this rib for the purpose of keeping a barge in position, which
+certainly did occur, gave the arch rib just such an additional strain as
+to result in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The inner ribs
+were of a much less objectionable section.
+
+[Illustration: FIG. 84.]
+
+Cast-iron arches, though still allowed by the Board of Trade rules, are,
+indeed, liable to be seriously affected by settlement, or yielding of
+the abutments, unless hinges at the crown are introduced. As an instance
+of this may be quoted a bridge of some 45 feet span, in which the arches
+were cast in two pieces abutting, and very efficiently bolted together
+at the crown, the springing and vertical abutment member of the
+spandrel being bolted and built solidly into heavy masonry. The arch
+sank at the crown, caused by, or itself the cause of, a movement of the
+abutment, with the result that the lower bolts at the crown joint broke
+away, rupturing the casting, as shown in Fig. 84. The arch must then
+have acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if a proper
+hinge had originally been provided. The break happened to occur so as to
+leave a sufficiently good bearing face at the crown; there was, indeed,
+no tendency for one surface to slide upon another; but in the accidental
+fracture of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.
+
+A second case of very much the same character has also been under the
+author’s observation, though in this the ends of the spandrels were not
+built into the brickwork of which the abutments were composed. Other
+instances of fracture either in the arch proper or in the spandrel work,
+have come under notice, though particulars cannot now be adduced; but
+the examples cited are by themselves sufficient to justify the
+conclusion that it is imprudent to construct a cast-iron arch without a
+central pin or its equivalent, unless the abutments, being exceptionally
+well founded, may be relied upon as free from any liability to move. It
+is, however, to be borne in mind that movement in the abutments of a
+small arch of any given absolute amount is more injurious than the same
+amount of movement in the abutments of large arches of similar design,
+so that what may be negligible in the latter case would perhaps be
+destructive in the former.
+
+To the absence of ductility and liability to initial stress must be
+added yet another disadvantage to which cast-iron work is prone--viz.,
+the possibility of concealed defects, blow-holes or cold-shuts; these in
+good foundry practice are not very likely to occur, but, as they are
+possible, cannot be overlooked in considering the suitability of cast
+iron for bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks by way of
+qualification, the author reiterates his opinion that there is still a
+use for cast iron in bridgework.
+
+With respect to the repair of cast-iron bridges, but little is to be
+said; the possibilities in this direction are very limited. Occasionally
+it may be desired to deal with the fracture of some member in the
+spandrel bracing of an arch, when it is commonly sufficient, and even
+preferable, to limit the repair work to confining the fractured parts in
+such a way as to prevent displacement.
+
+Rarely it may happen that an arch fractures as a result of settlement,
+or other movement, when, if it is decided that safety of the structure
+is not imperilled, it will in this case also be preferable to confine
+the parts simply by flitch-plates or other contrivance, with no attempt
+rigidly to make good the break, the consequences of which treatment
+would probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable, though
+something may occasionally be done by the negative process of lightening
+the dead load, or by remodelling the permanent way. Arches may, however,
+be rendered much more reliable by the introduction of suitable bracing
+where this is either wanting or inefficient.
+
+In scheming such additions it is desirable to arrange for as little
+drilling of the old work as is possible; where this cannot be altogether
+avoided, the position of the holes should be carefully chosen with
+regard to the effect they may have upon the strength of the old work.
+
+
+
+
+CHAPTER XIII.
+
+TIMBER BRIDGES.
+
+
+Timber bridges, though probably the most ancient in type, are yet the
+least durable in any particular instance. The perishable nature of the
+material when used for exposed construction renders it peculiarly liable
+to develop defects which quickly put a limit to the life of the
+structure. In addition to decay in the body of the main members--which
+may perhaps be long delayed, so that a simple beam bridge may last for
+many years--there is in more complex designs decay at connections and
+joints, which proves very detrimental to the integrity of the whole.
+Water running upon the surface of a member gravitates to its lower end,
+and, if there be a joint or other connection, settles there, to be
+productive of lasting mischief. From this cause, together with a very
+common deficiency of bearing surface relative to the forces to be met,
+the joints soon develop some movement; working of the structure
+commences under passing loads, its final destruction being then a
+question of time only. Each joint is, in fact, in timber bridge
+construction a source of serious weakness to a degree which has no
+parallel in well-designed metallic bridges.
+
+Wrought-iron straps to confine the ends of raking members, or for other
+uses, are liable to crush into the wood, and bolts are apt to enlarge
+the hole through which they pass. Wood keys, where these are introduced
+to prevent one timber from sliding upon another, are also prone to
+develop cracks in the main members, and fibre crippling from excess of
+stress. All these defects are, however, in timber-work more easily
+defined than efficiently remedied, as it is barely practicable for any
+but the harder woods to ensure, for heavy loads, a sufficiency of
+bearing surfaces.
+
+The most readily detected evidence of deterioration in timber bridges is
+the sag of its bearing members, or trusses, for the simple reason that
+if there is no local trouble at the joints, there will probably be no
+appreciable drop at the centre of the span. The existence of such a
+depression may, however, be caused in rare instances by the spread of
+the supporting piers or abutments, particularly in the case of beams
+trussed by end diagonal rakers and having no tie.
+
+Bridges formed of deep trusses, with the road upon the top, are
+sometimes found to be wanting in lateral bracing, the result of which is
+that the main trusses go out of line, leaning considerably one way or
+the other, being checked only by such rigidity as the joints and
+floor-beam attachments may have, with possibly some assistance from the
+end connections of the span.
+
+The decay of piles where entering the ground or water is, of course, a
+fruitful source of trouble, as also is the sinking of piles, where these
+are insufficient in number, or have not been well driven in the first
+place.
+
+A vital difficulty with timber structures generally is the uncertainty
+that will commonly exist as to how far decay extends in those cases
+where it has started. Timber does not necessarily show upon its surface
+the evidences of internal rotting. Memel timber may, indeed, be
+sometimes found to have become thoroughly unreliable, yet showing no
+sign of this upon its painted surface. By sounding the wood with a
+hammer, or by probing, its condition may commonly be ascertained. In
+cases of doubt, an auger-hole will make it clear as to whether the
+interior be good or otherwise, as to the particular parts tested; but
+only as to those parts, leaving it a matter of guesswork as to the
+remainder.
+
+[Illustration: FIG. 85.]
+
+A railway bridge having many of the defects which have been indicated
+may be quoted as an example. This structure crossed a canal, supported
+upon piles, some of which were in water, others carrying land spans. The
+canal span consisted of four trusses, one under each rail, or nearly so,
+framed in the manner shown in Fig. 85, precise details not, however,
+being now available. The trusses, apart from deflection under live load,
+sagged considerably--in one instance, 4-1/2 inches; one inside truss was
+also leaning towards the centre line of the bridge as much as 3 inches.
+One raker, or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections and joints
+were also in a bad condition. The vertical tie-bolts of the main trusses
+were all slack. The piles generally, many of which were badly decayed,
+had sunk and inclined towards one end of the bridge about 4 inches in 7
+feet of height, the ground being soft and unreliable.
+
+Movement under a passenger train crawling over the bridge was very
+appreciable, but not startling. There had been introduced, from time to
+time, additional timbers and iron ties, with the object of rendering the
+spans more reliable, but leaving it somewhat difficult to determine the
+function of the several members. The bridge was, of course,
+reconstructed.
+
+[Illustration: FIG. 86.]
+
+[Illustration: FIG. 87.]
+
+[Illustration: FIG. 88.]
+
+An instance may here be cited showing how badly distorted a timber
+structure may become without actually falling. The bridge referred to
+consisted of three spans of 29 feet, each span having two trusses,
+between which ran a colliery tramroad, 1-foot 6-inch gauge; the corves
+running upon this, at 4 feet 6 inch centres, weighed, when full, about
+10 cwt. each. The trusses were badly out of shape, the centre span
+having sagged 5-1/2 inches, with one truss of the same span nearly 10
+inches out of line at the centre. This little bridge, of which some
+details are shown in Figs. 86, 87, and 88, had been in use about twenty
+years.
+
+[Illustration: FIG. 89.]
+
+A third case which may be named is that of a road bridge, about 12 feet
+wide, crossing by thirteen spans a shallow river liable to floods. The
+construction was of a simple character, as indicated in Fig. 89, and
+consisted of piles supporting trussed beams, which had sagged in some
+instances over 2-1/2 inches. The bridge had, some years previous to the
+author’s inspection, been heavily repaired, many new strut and
+stretching pieces having been introduced, the piles also being
+reinforced or renewed. Five years before, a traction engine, said to
+weigh 5 tons, had passed across the bridge in safety; but the author
+noticed that a coal wagon, which, with the horse, weighed about 50 cwt.,
+when walked slowly over set up much movement. This bridge had been in
+use nearly thirty years, and was very much out of line from end to end.
+
+Though timber bridges cannot at the best be considered durable, yet, by
+attention to certain points in design and construction, their length of
+life may be materially enhanced. Every cut across the grain may be
+considered an element of weakness by exposing the material to quicker
+decay, for which reason the number of ends, or of joints, should be
+reduced to a minimum. An additional reason for reducing the number of
+joints or other connections is the liability of these to develop
+movement, as already stated, the yield of any one joint, being the cause
+of movement in others, which might, but for this, have remained close.
+These considerations lead to the conclusion that fewness of parts is, in
+timber construction, as in structural work generally, an excellent
+principle to observe. Mortising, elaborate scarf joints, recessing, or
+any cutting into the timber which is not essential, should be avoided,
+the simplest forms of connection being preferable, if at all suitable.
+If a step or butt surface is wanted for any member, it is commonly
+better to provide this by a cleat or other added piece, rather than by
+cutting into the timber butted against.
+
+A complicated joint formed in the body of main timbers can only be
+renewed by renewal of the timber itself, whereas by the method indicated
+the joint is readily tightened, or re-made, without involving the main
+member. Bearing surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake of bearing
+surface in the holes, and reduction of any liability to bend under
+cross-stress. In trusses of the form shown in Figs. 85 and 86, it is
+desirable to introduce diagonal members in the middle bay, even though
+it may appear that the stiffness of the main beams is sufficient to
+render this unnecessary as a matter of strength, as without these there
+is apt to be, under rolling load, a slight distortion, leading to
+working of the joints and free entry of moisture. Lateral bracings
+should also, for much the same reasons, be introduced, even though they
+may not appear necessary in the new structure, with joints all close and
+effective.
+
+Projecting ends of timbers should be carried out well beyond the
+requirement of strength or bearing, in order to ensure a liberal margin
+for that decay in the end fibres which commonly develops. Timbers
+resting upon abutments, or running into confined spaces, should be
+arranged for free ventilation and ready drying. Occasionally joints at
+the lower ends of timbers are protected by lead or zinc flashings to
+prevent water running into them, a method which should have some
+protective value. Whatever measures may be adopted, whether in the
+design or execution of timber bridge-work, will, however, be but little
+effective, if the timber itself is not good of its kind, and well
+seasoned.
+
+Creosoting to be useful should be thorough and something more than skin
+deep. The timber itself should be well dried before treatment.
+
+The repair of timber bridges very largely consists in the renewal of
+decaying timbers, where this is practicable, or in adding supplementary
+pieces where the old cannot conveniently be displaced. Joints may be
+tightened up by hard-wood wedges, properly secured to prevent slacking
+back, all bolts being also screwed up tight, perhaps some additional
+being introduced.
+
+Piles standing in water, which have decayed, may be strengthened by
+driving other piles between the old, or on either side, but not of
+necessity opposite to them, and by means of waling timbers bolted to the
+old piles, put in a position to take load, either by the walings resting
+upon their tops, or being bolted to them. Piles decayed where entering
+solid ground may generally be strengthened by bolting on supplementary
+timbers to reach well above and below the decayed part, or by cutting
+out the bad length, introducing a new piece, and fishing the butt-joints
+in a proper manner. But all remedial measures have generally to be
+considered with reference to cost, as compared with the probable
+increase of life of the structure. With a bridge in an advanced state of
+decrepitude, such repairs may prove anything but economical, and at the
+best defer reconstruction but a very moderate length of time.
+
+
+
+
+CHAPTER XIV.
+
+MASONRY BRIDGES.
+
+
+Masonry bridges, in which description it is intended to include
+structures both in stone and brick, are, when well built, amongst the
+most durable and long-suffering of any which come under the care of a
+maintenance engineer; yet when developing the faults peculiar to their
+kind, they may be the occasion of much anxiety, and render necessary
+frequent inspection, or even continuous watching.
+
+Apart from decay of mortar or material, defects may very commonly be
+traced to the foundations, or to earth-slips. Sinking, when uniform, may
+be quite harmless, though possibly inconvenient; irregular sinking of
+piers or abutments is quite a different matter. It is, however,
+remarkable to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and kind which would
+be fatal to the connections of metallic bridgework is endured by bridges
+of stone or brick; not, it may be, without damage, yet with no occasion
+for alarm. The superstructure of metallic bridges may often, however, be
+restored to the true level before the mischief has become serious,
+whereas in the case of masonry arches this is not practicable.
+
+Spreading of the abutments is very seldom the cause of any great injury
+to an arch, though it is common enough to find old and flat arches
+slightly down at the crown; but the contrary case of abutments closing
+in is not very unusual when these are high, or terminate a viaduct over
+a deep valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected; or, if the
+arches are very solid and heavy, the abutment may slide forward at the
+base, with no sensible reduction of the opening.
+
+When a viaduct connects the two ends of a high embankment, it may happen
+that the end piers are not clear of the embankment slope, in which event
+a pier may, should the bank slip, move with it, as to that part not in
+solid ground; with the result, in a bad case, that it is broken across
+and the superstructure imperilled.
+
+[Illustration: FIG. 90.]
+
+A case of abutment movement is illustrated in Fig. 90, which represents
+the end arch of a masonry viaduct, one abutment of which had moved
+forward in the manner already referred to. From the springing upwards
+the arch retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the movement became
+pronounced, heavy timber centering was introduced, with the object of
+preventing any mishap, the damaged portions being ultimately cut out and
+made good. The structure was thirty-five years old.
+
+The practical utility of stop piers in long arched viaducts is, perhaps,
+rather in checking movement of the tops of piers under moving load than
+in arresting actual failure of a series of arches. That the tops of
+piers do move very sensibly need not be doubted. The author has
+attempted to measure this in the case of piers about 60 feet to the
+springing, by means of a theodolite placed below, but has reached no
+more definite result than that a movement existed, of which he was not
+able to determine the amount. If in a viaduct some arches are more
+heavily loaded than others, each spreading slightly, the end piers of
+the group will move amounts which together equal the sum of the
+individual span spreads, with a tendency in the arches beyond those of
+the group overloaded to rise.
+
+This rocking may be detrimental both to the piers and arches, and helps
+to account for the disintegration of mortar in arches and piers, which
+not infrequently happens. The soffits will sometimes be seen with a
+thick incrustation of lime, which has washed out of the joints, or from
+limestone ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that pieces of stone
+or brick will drop out, necessitating repair at heavy expense, of which
+scaffolding is commonly a large part.
+
+Tall piers may be found badly out of the upright due to sinking of
+foundations. A marked case of this kind came under the author’s
+notice--a viaduct of fifteen semicircular arches, in which, though many
+piers were wanting in truth, one in particular was about 1 foot 4 inches
+out of vertical, making one side of the shaft plumb, and doubling the
+normal batter of the other. Inquiry showed that in this instance the
+pier had never been upright from its earliest history dating back
+thirty-six years. This makes clear the desirability, to avoid hasty
+conclusions, of ascertaining, when it is possible to do so, the complete
+record of any structure.
+
+A bridge fifty-eight years old, of three skew spans, carrying a railway
+over a canal, and having somewhat flat brick arches with stone quoins
+upon low piers, developed the somewhat unusual defect, as to the centre
+arch, of splitting along its length for about 10 feet, parallel to and
+some 7 feet from one face. In this case there was reason to believe that
+there had been considerable local settlement of the piers on that side
+of the bridge. The arches were otherwise in bad condition, the brickwork
+poor, and the mortar decayed. Each arch was down at the centre, and
+displayed a fault not unusual where bad brickwork joins up to good cut
+stonework, the quoins showing a tendency to separate from the brick
+rings. Below the bridge were coal-workings.
+
+Brick arches built in parallel rings sometimes separate one ring from
+the other, demonstrating the known propriety of bonding the rings
+together properly, and of carrying the arch round, when building, at its
+full thickness.
+
+[Illustration: FIG. 91.]
+
+An instance of bridge failure from a somewhat peculiar cause may be
+quoted as of some interest, largely because the structure was very
+ancient, having been in existence some 400 years. This bridge, carrying
+a road, was of the type usual in old masonry bridges over a river,
+having small arches, thick piers, and solid backings to the arches. Two
+flood-openings at one end had, by sinking and want of care, become
+partly closed. The centre arch had, however, been widened about 140
+years previously. During a severe flood, the swollen river, overflowing
+its banks, trespassed upon a timber yard a little above bridge, and
+washed down into the stream a large quantity of sawn timber; this,
+unable to get through the main arch with freedom, compacted into a
+serious obstruction. The flood water, thus checked in its passage, seems
+to have scoured below the timber, and robbed the piers of such support
+as they formerly had (see Fig. 91). The bridge stood in this condition
+till the water lowered, when the middle part of the structure broke up,
+and subsided into the hole which had been washed out. But for the
+monolithic character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers stood had
+been partly undermined for very many years. The case is instructive, as
+showing how a slight accident--powerless by itself to work mischief--may
+be very damaging when allied with so powerful an agent as running water.
+
+[Illustration: FIG. 92.]
+
+The enduring character of even the roughest class of masonry arch, if
+only the material be good and abutments stable, is shown when it becomes
+necessary to destroy old work of this character. Fig. 92 represents a
+short length of “cut and cover” arching in process of demolition, just
+before it fell in. The masonry was of hard sandstone rubble and had been
+cut away, as shown, till at the point A only a very small piece of the
+arch remained, when the length finally broke up and dropped. Arches have
+commonly a great reserve of strength; tunnel linings are, indeed, often
+badly out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed or bulged,
+to serve the purpose intended.
+
+Though the equilibrium of masonry arches has been the occasion of much
+profound study, and the nicest calculation has sometimes been applied to
+the design of such work, yet it appears that when an arch is well backed
+up, the theoretical linear arch need have but little connection with the
+figure of the intrados; a statement consonant both with common-sense and
+the teachings of experience. With solid backing, this would indeed seem
+to be more important than any part of the arch ring below the top of the
+backing, the lower part of the ring serving chiefly to preserve the face
+of the solid work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure would seem to
+be inevitable. The masonry or brickwork does not always show evidence of
+damage, if the distortion has been slow; suggesting that structures of
+this kind have a power of accommodation with which they are not
+generally credited.
+
+A noticeable cause of deterioration of masonry structures, which may be
+quite independent of settlement, is serious vibration. This is well
+known in connection with church belfries, and is also locally apparent
+when telegraph or other poles are attached to masonry parapets.
+Vibration, when caused by heavy railway traffic, acting upon arches
+light or originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially built, and
+particularly those carrying ordinary roads, and not subject to much
+vibration, have great lasting powers, if repaired with skill, or even
+let alone. Distortion of the arch may be quite consistent with practical
+stability, if the movement or decay with which it originated is not
+progressive, or has been arrested. In this connection a distinction is
+to be made between arches well backed, to which the foregoing remarks
+apply, and in which the two halves of each arch may act as separate
+monoliths meeting at the crown, and the case of a true arch ring
+independent of any outside resistance, such as backing or spandrels may
+give, and depending almost wholly upon the proper balance of its
+component voussoirs for its stability. With the latter class of
+structure no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way, and the work
+is dealt with judiciously, if at all. It must, however, be understood
+that there are limits as to what may be done effectively, short of
+rebuilding, in dealing with structures in which, perhaps, brickwork is
+rotten and mortar decayed and crumbling, the whole being little better
+than a broken mass of rubbish.
+
+In cases where it may be prudent to introduce safety centring, as in an
+instance already referred to, it is commonly expedient to refrain from
+causing this to take any sensible part of the load till all movement has
+ceased, the centres being at the outset largely precautionary. The
+requirement with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement is still going
+on, the effect may be to cause the arch to break up upon the centring,
+and precipitate repair work which might otherwise have been left to a
+more convenient time, when all movement had stopped or been checked by
+suitable measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt with
+piecemeal by cutting out the bad places, a small part at a time, and
+making good. The work requires the greatest care of experienced men.
+
+Pointing masonry or brickwork is effective for little other than
+protective purposes, and to check further weathering; it has obviously
+no effect upon the interior work, and if made to cover up the evidences
+of internal decay, is even misleading and objectionable. In extreme
+cases it may be desirable to open out the road and deal with the
+filling, to relieve or to strengthen the outer spandrel walls, which
+sometimes bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise repairing solid backing,
+in which operations some regard must be had to the effect of the work
+upon the balance of the opposing halves of the arch.
+
+Of the different classes of masonry commonly used in bridgework, it may
+be well to remark that good coursed rubble, or preferably that variety
+bonding both vertically and horizontally, of a durable stone, perhaps
+quite unfit for any but rough dressing, may make a most lasting
+structure, the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from the block,
+probably along some line of relative weakness--there is no “nursing” of
+weak corners; whereas with stones reduced to a perfectly regular shape
+by chisel work, the plane surfaces and geometrical angles are made with
+partial regard only to the natural grain of the stone.
+
+
+
+
+CHAPTER XV.
+
+LIFE OF BRIDGES--RELATIVE MERITS.
+
+
+The life of bridges of differing materials has been incidentally touched
+upon by the examples quoted, in dealing with each class of structure. It
+will be useful to recapitulate some of the facts adduced, and to compare
+the terms of life so far as they appear to be indicated; but in doing
+this it is necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history. The
+duration of any such structure may be limited by adverse conditions,
+peculiar to the case considered, by defects of design, material, or
+workmanship--present from the first--or by neglect, overloading, or
+accident, making up its later record.
+
+With the exception of timber structures, it is difficult to find any
+class of bridges furnishing examples which have reached the limit of
+life, independently of the evils named, and as a result of unavoidable
+decrepitude. There are none the less influences at work tending to this
+condition, and which it is too much to expect can in all cases be
+foreseen or completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and minor
+faults in design, which even in the most capable hands may be expected
+ever to fall short of perfection. At the best, then, the life of any
+structure, though long, must have a limit. With bridges of more average
+or inferior qualities the life may be positively short, even without the
+destructive influence of overloading.
+
+Dealing with instances of metallic bridges, the adjacent table gives the
+time each had been in existence when removed, and some indication of the
+reason for its condemnation. Those marked with an asterisk were cases of
+pronounced high stress. From a study of the table it appears that in
+actual practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and thirty-six
+years; but these figures applied to this collection of cases only. It is
+to be remarked that many other bridges outlasted these, and are likely
+to continue reliable. These results show, then, no more than that some
+wrought-iron bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as indicating that
+the durability of such structures is by no means so limited as the table
+would suggest. It is to be observed that, as design and maintenance are
+now better and more generally understood than when experience was
+largely wanting, it is to be expected that later examples will show no
+such poor results.
+
+Of steel bridges little can be said, because of the limited time this
+material has been in use; but the generally acknowledged belief, quite
+in agreement with the author’s observation, that steel rusts more freely
+than wrought iron, suggests that such bridges will have a shorter lease
+of life, the more so that the surface-to-section ratio is also greater
+for higher unit stresses, though other adverse influences are much the
+same for one material as for the other.
+
+Of cast-iron structures but few cases have been given; of these,
+cast-iron arches have been noticed as developing defects which led to
+reconstruction, or to limiting the loads to be carried. Plain cast-iron
+girders, on the other hand, have never, under the author’s direct
+observation, been removed for any other reason than because they were
+cast iron, or from over-stress, due to the growth of loads; never from
+defects or wasting, though it is not suggested no such cases exist. The
+author has no evidence which points to what may be the limit of life of
+a good cast-iron girder fairly treated.
+
+_Examples of Life of Metallic Bridges._
+
+  -------------------------+-------+------+----------------+------------
+        Description.       | Span. | Age. |   Defect.      | Reference.
+  -------------------------+-------+------+----------------+------------
+                           |ft. in.|Years.|                |
+                           |       |      |                |
+                                _Wrought Iron._
+                           |       |      |                |
+  Plate girders            |  (?)  |  12  |Loose rivets    |
+    *Ditto                 | 35  0 |  12  |Ditto           |p. 52
+     Ditto                 | 55  0 |  14  |Rust. Distortion|pp. 78 & 97
+  Trough girders           | 11  0 |  16  |Loose rivets.   |p. 50
+                           |       |      |Cracked webs    |
+  Plate girders            |  (?)  |  22  |Loose rivets    |
+  Twin girders             | 31  6 |  23  |Weak. Cracked   |p. 13
+                           |       |      |webs            |
+     Ditto                 | 35  6 |  23  |Weak. Distorted.|p. 74
+  Plate girders            | 42  0 |  23  |Loose rivets.   |p. 21
+                           |       |      |Cracked webs    |
+     Ditto                 | 72  0 |  29  |Weak. Loose     |p. 53
+                           |       |      |rivets          |
+     Ditto                 | 47  0 |  24  |Distortion      |p. 9
+     Ditto                 | 32  0 |  32  |Rust. Cracked   |p. 14
+                           |       |      |webs            |
+    *Ditto                 | 25  0 |  36  |Weak            |p. 63
+                           |       |      |                |
+                                  _Steel._
+                           |       |      |                |
+  *Trough girders          | 15  8 |  32  |Weak. Rusted    |pp. 68 & 98
+                           |       |      |                |
+                                _Cast Iron._
+                           |       |      |                |
+  *Girders                 | 32  0 |  36  |Weak            |p. 141
+   Girders, cast-iron piles|  (?)  |  44  |Ditto           |
+   Arches                  | 45  0 |  55  |Crack. Settle-  |p. 145
+                           |       |      |ment            |
+     Ditto                 |100  0 |  62  |Crack. Deforma- |pp. 80 & 145
+                           |       |      |tion            |
+  -------------------------+-------+------+----------------+------------
+
+With timber bridges the length of life appears to be about twenty-five
+years, but this is very largely dependent upon the question of
+maintenance, and may range from fifteen to thirty-five years. It is
+manifest that repairs, when extensive and consisting of the renewal of
+the more essential parts of the structure, border upon reconstruction,
+and may be continued indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for railway
+bridges, be taken as stated, though for highway bridges possibly longer.
+
+Of masonry bridges little is to be said but that it is only in cases of
+bad work or material--with, perhaps, vibration or settlement--that these
+have a shortness of life comparable with that of defective metallic
+bridges. Where these adverse conditions obtain, heavy repairs may be
+necessary before the structure is many years old; but, under reasonably
+fair conditions, bridges of masonry may be expected to outlast
+structures in any other material. Apart from road-bridges which are
+admittedly long-lived, there are a large number of railway bridges and
+viaducts of masonry which, despite heavy loads and vibration, have been
+in use for the past seventy years.
+
+Dealing with the cost of maintenance, this with bridges of wrought iron
+or steel should result simply from scraping and painting, with such
+other incidental work as may be necessary on the subsidiary materials
+used in the structure. The cost of painting will vary with the height
+and character of the bridge, and the amount of scaffolding, if any, and
+may be from 5_d_. to 1_s_. or more per square yard; this if distributed
+over five years, a not unusual interval between each painting, works out
+at an appreciable figure, which may vary from one-third to one per cent.
+of the first cost, per annum. The yearly cost of painting steel-work
+will, for shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be necessary,
+repairs and possibly strengthening, which may raise the total cost of
+maintenance very considerably.
+
+Cast-iron bridges, being less liable to rust, cost less for painting
+than other metallic bridges; and if the cast iron is closed in by
+masonry, practically nothing; they do, indeed, involve very little
+expenditure in the maintenance. Not being very amenable to repair or
+strengthening, cast-iron bridges commonly remain very much as built, or
+are reconstructed.
+
+The proper care of timber bridges may become costly as the structure
+gains in age, and soon grow to a very wasteful expenditure. This is
+evident when it is considered that repairs may be necessary after ten
+years, and that whatever may have been the cost of any part when new, it
+cannot be replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions to be
+observed in dealing with an old structure carrying its load. In addition
+to ordinary repairs, there will be paint or other protective coating to
+be applied, though this is not always done.
+
+The upkeep charges of masonry bridges will be practically nothing in
+favourable cases; but, on the other hand, where extensive repairs become
+necessary, may reach a considerable amount. Exceptional outlays are,
+however, infrequent, and may be spread over a large number of years, in
+those rare instances in which they become imperative.
+
+  _Durability._      _Maintenance     _First Cost._
+                     Charges._
+
+  Masonry            Masonry          Timber
+  Cast Iron          Cast iron        Masonry
+  Wrought iron       Wrought iron     Steel
+  Steel              Steel            Cast iron
+  Timber             Timber           Wrought iron
+
+For purposes of ready comparison, placing bridges of the materials under
+review in order of durability, they would appear as in column 1 of the
+table above; in order of low maintenance charges, generally as in column
+2; and in order of low first cost, as in column 3. With respect to the
+question of first cost, the arrangement of the third column applies only
+to small bridges, say, up to 70-foot span; and, being liable to
+variation with the conditions, is but approximately correct. The less
+costly descriptions of masonry are alone considered in this connection.
+
+It may be added that the total yearly charge of interest on first cost,
+redemption, and maintenance, appears to be for masonry bridges, about
+one-half only of the corresponding totals for bridges of wrought iron,
+steel, or timber; those of cast iron taking an intermediate place.
+
+Summarising the above considerations, and dealing with the relative
+merits of bridges in the different materials, it may be broadly stated
+that for conditions at all suitable nothing seems to be superior to
+masonry--including in this description first-class brickwork--whether
+for road or railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little affected by
+increase of loads. The mass of a masonry arched structure is so great,
+and the margin of strength commonly so liberal, that considerable
+increments of load may have but little effect upon the reliability of
+the structure.
+
+Cast iron has, for bridges of simple design, a strong claim to the
+second place, though its want of ductility is a demerit. It can,
+however, have but a limited use in bridge construction, being applicable
+only to small girder spans and skilfully-designed arched structures.
+
+For bridges of moderate span in which the question of cost does not
+control the matter, wrought iron should probably come next, steel being
+best reserved for those of a larger size, in which weight of the
+structure greatly affects economy.
+
+Timber may be regarded as a material rarely to be used in this country
+for structures to occupy a permanent place, unless for urgent economic
+reasons of the moment.
+
+While expressing this general view of the matter, it is to be admitted
+that the propriety of these conclusions is somewhat discounted by the
+difficulty there now is in obtaining cast iron of the desired
+toughness, or wrought iron with promptitude and sufficient variety of
+section at a reasonable price.
+
+It is apparent, also, that the choice of material may be largely
+influenced--even determined--by considerations of headway, construction
+depth, or character of foundations; so that no very definite rules can
+be usefully laid down, though the adoption of unsuitable materials has
+not been so unusual as to make these suggestions altogether
+purposeless.
+
+
+
+
+CHAPTER XVI.
+
+RECONSTRUCTION AND WIDENING--CONCLUSION.
+
+
+The need for the reconstruction of bridges, arising from various causes
+which have been treated in the preceding chapters, original weakness or
+faults in design, decay or defects, may also be caused by such
+extraneous considerations as the growth of loads, widening of the
+openings spanned, or improvement of the headway.
+
+In any case, a precise survey or measuring up of the structure and its
+immediate surroundings is required, in the execution of which the
+greatest care is desirable, and with respect to which it may be well to
+give a few hints.
+
+The surveying chain, when used, should be tested, the measure of
+accuracy required rendering this imperative in a degree peculiar to work
+of this class. Linen tapes should also be compared with a reliable steel
+tape, and used only where sufficiently accurate for the particular
+purpose. A careful and observant man may do very good work with a linen
+tape, making just that allowance in the sag of the tape which corrects
+for the inevitable stretch; but there is still some uncertainty involved
+in its use, and the author prefers to rely upon a steel tape,
+notwithstanding the inconvenience commonly experienced from its
+intractable nature and liability to damage.
+
+Instruments used must also be in the best adjustment; as errors, which
+in ordinary field work may not be of great importance, are inadmissible
+in bridge work.
+
+It is not necessary here to enter upon the methods of small survey
+work, but it may be desirable to point out that abutment walls should be
+plumbed for verticality; girders, which are liable to be leaning,
+defined in position by reference to their bearings; and generally that
+it should never be taken for granted that there is truth in old work, or
+that this may be assumed as to line or level.
+
+In cases where disputes with any local authority as to headway are
+likely to arise, it is prudent to supplement the information as to level
+of soffits by rods cut to length in strict agreement with the clear
+height, before removing the old superstructure.
+
+It is apparent that in cases where the superstructure is already
+condemned, the detail measurements may be confined to that part of the
+structure which is to remain, securing only such information as to the
+work superseded which may be required in arranging for the new work.
+
+In taking particulars of skew bridges, needless as the warning may seem,
+it is yet necessary to remark that there may be right or left-hand skews
+which will not reverse. The author has known a disregard of this to make
+serious trouble in two instances.
+
+Dealing first with reconstruction of the superstructure of railway
+under-bridges, these, if small, may not give much trouble, though the
+demand for greater strength will, perhaps, involve some difficulty in
+working to the limiting construction depth--i.e., the distance from the
+top of rail to soffit of bridge--particularly as many old bridges have a
+very niggardly allowance in this respect. It may be, and quite commonly
+is, necessary to raise the rails a small amount, or, if headway is not
+restricted, to lower the soffit. Clearances between the running gauge
+and girder-work may also be difficult to secure, more liberal allowances
+being now required than formerly. Complications in the character of the
+permanent way, so frequently found upon old bridges, should, of course,
+be got rid of, if possible; but the endeavour may introduce further
+difficulties. Regard must throughout be had to the methods to be adopted
+in removing old work and in erecting the new. Perhaps the simplest case
+to deal with is that where girders lie parallel to, and under the rails,
+with a timber floor upon which the permanent way is carried, as sections
+of the road involving pairs of girders may be readily removed, and
+replaced by the new girder-work (see Fig. 93). If the deck be of trough
+flooring or old rails, the matter may not be so simple, as regard must
+then be had to the position of joints in the existing floor, and the new
+work be schemed with respect to the number and office of girders which
+may be got in at any one breaking of the road. A slight slewing of rails
+may sometimes be resorted to on occasion, where this has the effect of
+releasing some part of the work not otherwise to be dealt with.
+
+[Illustration: FIGS. 93 and 94.]
+
+Bridges having main girders, with timber or trough flooring resting upon
+the bottom flanges, or suspended by bolts, will, if carrying many roads,
+cause some little difficulty, as the dismantling of any one span
+involves the disturbance of others; where, however, many lines are
+concerned, it may be feasible to put one or more temporarily out of use,
+preserving the continuity of traffic over those which remain, but
+refraining from any diversion of the more important roads.
+
+Somewhat similar troubles occur where main girders with cross-girders at
+the lower flanges are found, particularly if the cross-girders are
+arranged in line, the ends abutting on each side of the same main girder
+webs. It is seldom, however, that this construction is used in bridges
+of small span carrying many roads; but where it does occur, it may
+necessitate the use of timbering below, to carry the ends of
+cross-girders when freed from their supporting main girders. (See Fig.
+94.)
+
+[Illustration: FIG. 95.]
+
+If it is proposed to use new main and cross-girders, it is desirable to
+arrange these in the manner already recommended, the cross-girders not
+in line; this has peculiar advantages in reconstruction work, as the
+bolting up and riveting of the cross-girder ends is not hampered by
+other cross-girder attachments, leaving each piece of floor complete in
+itself. Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence of
+one span from those adjoining (see Fig. 95); but the method is wasteful
+of space, and involves a somewhat greater total weight in the main
+girders.
+
+The foregoing observations apply more generally to small single-span
+bridges, the operations on which may be effected without any material
+disturbance of traffic arrangements; though this can seldom be wholly
+avoided, it should be confined, where practicable, to a few hours on a
+Sunday.
+
+The reconstruction of bridges over 70-feet span may have to be dealt
+with under more elaborate arrangements, if carrying two lines only,
+possibly with single-line working for a period more or less protracted;
+or it may be necessary, having regard to the weight of main girders to
+be removed, to carry the whole structure upon temporary staging,
+supporting the road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed erection in
+its ultimate position, or by erection at one side and drawing across.
+The latter method is, however, commonly reserved for cases in which no
+special staging is used under the old structure.
+
+Bridges of a number of openings are usually dealt with by securing full
+possession of one road at a time, which for double-line bridges
+necessitates single-line working. It is commonly out of the question,
+even with moderate spans, to deal with some of these only at a time, and
+so avoid continuous possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new main
+girders do not in any way interfere with those of the old, and where it
+is not necessary to reset bed-stones, or make other alterations in the
+bearings which necessitate the complete clearance of the pier-tops. In
+exceptional cases it may be found possible to arrange for the complete
+removal of a small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.
+
+Spans erected to one side of the final position, to be later travelled
+across, are commonly mounted upon gantry staging, and up to 50 tons
+weight may rest directly upon rails well greased. The power adopted to
+move the span is usually that of screw or hydraulic jacks, or
+occasionally engine haulage, special tackle being in that case necessary
+to apply the engine power in the right direction. If the time is
+limited, or weight considerable, a more elaborate arrangement by which
+the load is supported upon wheels, may be necessary, with a view to
+reducing the resistance to a manageable amount. All work which it is
+possible to do before shifting into place, including the permanent way,
+where this is of a special character, should be executed in advance,
+leaving only the rail connections to be made good when the span is in
+position.
+
+Where timber staging is used to carry the permanent way before
+dismantling an old structure, it is convenient to begin by placing stout
+balks of timber under the sleepers from end to end of the bridge, or
+directly under the rails if space is limited; the staging is then
+arranged to give support to the running timbers.
+
+Metallic under-bridges of ample headway, perhaps over coal-workings
+(since settled down), or for some less sufficient reason made of metal,
+may be cheaply replaced by brick arches built below the old
+superstructure, the springings of the arch being checked into the face
+of the existing abutments. With stout walls, careful work and good
+material will make this an efficient and durable job.
+
+It being a primary condition of reconstruction work to interfere but
+little with ordinary traffic arrangements, single-line working is
+avoided wherever practicable; as this, always objectionable, may
+necessitate the erection of special signals and signal apparatus,
+besides the temporary remodelling of the roads, and in this country may
+involve also a Board of Trade inspection--altogether a troublesome and
+expensive business.
+
+Any bridgework which is accompanied by breaking or blocking the road can
+only be undertaken by arrangement with the traffic department, after
+notice duly given and published in the periodical record of such
+matters; it is generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand as is
+possible. Wherever practicable and prudent, the whole work is released
+from its surroundings, masonry cut away, rivets cut out and replaced by
+good bolts, nuts removed from holding down bolts, or the bolts cut
+through, etc. Particular care should be exercised to ascertain what
+remains to be done immediately prior to removal. It is necessary further
+to arrange for trucks to be in readiness to receive old material, and
+others containing new girder work to be conveniently stationed, having
+been loaded up to come right end foremost; engine power, cranes, empty
+and loaded trucks, being all marshalled and so placed as to be available
+in proper order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or as to the
+reach of the crane in effecting its work.
+
+The whole operation to be conducted on any Sunday should be well within
+the resources of the men and plant engaged in it, or so managed that it
+is a matter of no serious importance if the whole cannot be completed as
+originally desired.
+
+Possession of the roads to be blocked having been secured between
+certain hours, if some part only of the work to be carried out has been
+completed as the time grows short, any attempt to execute the remainder
+may result in checking trains until such time as the line may be
+reported clear--a contingency to be avoided--though the temptation to
+save another Sunday’s work by delay of a few minutes to some one train
+may be considerable.
+
+In scheming any reconstruction, it may be insisted that at least one
+feasible method of carrying out the work must be secured, though it is
+the author’s experience that frequently some other method than that
+contemplated is in the end adopted, when, some months later, the final
+arrangements for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered, with a view
+to a moderate amount of work being done at any one time, and to achieve
+as much more as he can himself secure by scheming, or a liberal use of
+labour; all Sunday work, with attendance of engines and cranes, being of
+necessity expensive.
+
+Railway over-bridges do not commonly present any particular
+difficulties. The spans to be dealt with are usually small, and the
+weights to be lifted moderate. The height above rails may, however, be
+above the lift of any crane; and, for the purpose of raising main
+girders, a derrick may become necessary, the rearing and guying of which
+may block many roads during the time it is in use. The girders of larger
+spans, too unmanageable to be lifted whole, may be erected upon staging;
+to secure the requisite headway it may be necessary to build the girders
+at a level above that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the staging.
+
+The widening of railway under-bridges is, as a rule, a matter of no
+special difficulty, but some remarks may be of use. Widenings should be
+planned with a regard to later reconstruction of the original bridge, if
+that is at all likely to be necessary, and with the object that, when
+complete, the whole should be a consistent piece of work.
+
+It may, indeed, happen that widening of a bridge may involve the
+remodelling or reconstruction of the old work, to enable the new roads
+to be laid down as desired; this is more likely to be necessary where
+there exist main girders not competent to take any additional load, and
+to duplicate which would sacrifice space between the new and old roads;
+or it may be unavoidable because of slewing of the old rails, as part of
+a general rearrangement.
+
+[Illustration: FIG. 96.]
+
+Dealing with widenings simply, there is often some little trouble in
+contriving a connection between the new and the old work, as this may
+have to be made under, or close to, the sleeper ends of the existing
+roads. It is desirable to arrange this part so that no drilling of old
+work for rivets or bolts shall be necessary, there being, in fact, no
+strict connection. By judicious scheming, this may be effected, whilst
+securing freedom from leakage of water at the joint. (See Figs. 96 and
+97.) If tying of the new and old structure is desired, this can usually
+be done quite simply, well below the floor at some more accessible
+level.
+
+[Illustration: FIGS. 97 and 98.]
+
+The strict jointing-up of trough flooring, new to old, at right angles
+to the troughs, cannot be contemplated, but may be dealt with by
+treating each part independently, the ends being near together,
+separated by the space of an inch or so. Each trough end being closed up
+by a diaphragm or oak block to prevent ballast dropping through, the top
+of the space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions to
+take away leakage, as it is practically impossible to make this
+arrangement “drop dry” under the conditions common in executing work of
+this kind (see Fig. 98).
+
+[Illustration: FIGS. 99 and 100.]
+
+Where trough flooring, new and old, has to be made good parallel to the
+troughs, the difficulty of making a direct connection is less marked,
+and it is not unusual to introduce a strip cover simply; but if
+accessible, the work is still troublesome, as there is commonly a want
+of strict alignment and truth as to level, between the new and the old
+troughs. It is preferable to arrange for junctions of a more convenient
+type, as in Figs. 99 and 100.
+
+When widening masonry arch bridges by girder-work, it is desirable to
+insure that any girders parallel to the masonry face shall be
+sufficiently far removed from it to enable painting to be executed. The
+space remaining between the girder and the arch may then be bridged by
+floor-plates, or an extension of the timber floor if that is adopted.
+
+In effecting a junction such as this, the author has used the
+arrangement shown in Fig. 101, the advantage being that the piece of
+connecting-floor is sufficiently wide, and also sufficiently flexible,
+to allow the girder-work freedom to deflect without doing harm. The load
+carried by the width of floor is, as to one part, delivered well on to
+the old masonry, in preference to being imposed near to the face. If it
+should for any reason be imperative to place the girder close to the
+arch face, it is preferable to scheme the floor so that there shall be
+no actual contact, the new floor in that case slightly overhanging the
+masonry, as in Fig. 102, or dealt with as in Fig. 103, if depth is
+restricted.
+
+The widening of masonry arch bridges by masonry, calls for no other
+remark than that the new work should be free from the old; though it may
+be advisable, when the widening is narrow, to tie the new work to the
+old in such a way as to permit independent settlement.
+
+If the widening is exceptionally narrow, there may be no choice but to
+bond the new and old work together, and in the best manner, with the
+object of minimising the risk of separation.
+
+[Illustration: FIGS. 101 and 102.]
+
+[Illustration: FIG. 103.]
+
+The above matters relative to widenings, though apparently trifling, may
+by neglect cause much trouble and expense in maintenance. They
+principally concern small bridges, the extension of larger structures
+coming rather in the category of independent works.
+
+
+CONCLUSION.
+
+In bringing these chapters, dealing largely with questions affecting
+maintenance, to a close, it may be well to draw attention to the fact
+that economy in design (apart from improper reduction of sections) goes
+hand-in-hand with economy of upkeep. Given good material, that which
+favours low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to girders,
+favours also small expenditure in maintenance. The less complex the
+design, the easier will it be to keep the structure in order; the less
+the number of parts, the fewer will be the connections. Freedom from
+smithing eliminates liability to failure at cranks, or other work which
+has been subject to fire. It is apparent also that the free use of
+rolled instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A liberal depth
+to all girders, by reducing deflections, limits the inclination of the
+ends and gives the connections a better chance of remaining intact.
+Lastly, with work of this character, the labour of scraping and painting
+is simplified and cheapened.
+
+The author wishes to reiterate the statement made in the opening
+paragraphs of this book, that all instances of decrepitude, failure, or
+peculiar behaviour cited, have been under his direct observation. The
+fact is insisted upon simply that the reader may appreciate that the
+information is at first hand.
+
+It has not been thought necessary, nor was it considered desirable, to
+indicate the locality of each case referred to; but it may be said that
+the matter of these chapters has been accumulating during many years,
+and relates to structures under the control of many different bodies.
+
+The study of old bridges is strongly recommended, particularly with
+respect to stress and strain, which in structures new or old, occur
+possibly as may be expected--certainly as they must. Consideration of
+existing work may thus be a useful check upon the fanciful requirements
+of some methods of design. There is a recent tendency, for instance, in
+English practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many old bridges
+carrying their loads with no sign of distress, should have failed long
+ago. Excess in riveting is a common extravagance, to which the same
+criticism may in a less degree apply. Considerable impact allowances for
+girders of large span may also be referred to as an application of
+empiric theory not justified by experience, which, as in all cases where
+such considerations fight with facts, should be modified or rejected.
+
+
+
+
+INDEX
+
+
+  Abutments, leaning, 82, 173
+  -- movements of, 158
+  -- settlement of, 78
+  Adjustment of centre girders, 128
+  -- of distributing girders, 120
+  Angular distortions, 88
+  Arches, equilibrium of, 162
+  -- repair of, 163
+  Arrangement of cross girders, 21, 175
+  Asphalt, 26
+
+  Ballast, 29
+  Bearing pressure on rivets, 47, 51, 57
+  Bearings, skew, 4
+  Bottom booms, end bays, 18
+  Bracing, additional, 117
+  -- effects of, 34
+  -- flat bars, 37
+  -- incomplete, 41
+  -- sea piers, 42
+  Bridge floors, 20
+  -- repairs, 107
+  -- surveys, 107
+  Bridges, life of, 165
+  Breaks in [T] bars, 16
+  Buckling of webs, 16
+
+  Camber, 24, 80
+  Cast-iron arches, 80, 145
+  -- -- bridges, 141
+  -- -- columns, 7,144
+  -- -- girders, 141
+  -- -- in sea water, 101
+  Centre girders, 122
+  Cinder ballast, 29
+  Cold-blast iron, 141
+  Cooling stresses in cast iron, 145
+  Construction depth, 173
+  Corrugated sheeting, 29
+  Cost of centre girders, 135
+  -- of maintenance, 168
+  Counterbracing, 19
+  Cracked bedstones, 3
+  -- columns, 7
+  -- web plates, 13, 14, 15, 50
+  Cross girder arrangement, 21
+  -- girders, fixed ends, 22, 118
+  -- -- rusted, 29, 97
+  -- -- weak, 30, 66
+
+  Decay and painting, 96
+  -- of floor plates, 109
+  -- of timber, 28, 150
+  Deflection, 85
+  -- due to booms and web, 86
+  -- exceptional cases, 88
+  -- in new and old work, 85
+  -- working formulæ, 87
+  Deformations, 73
+  Depth of girders, 23, 89, 184
+  Diagonal ties, 19, 42
+  Distortion due to temperature changes, 79, 84
+  Distributing girders, 120
+  Drainage holes, 25
+  “Drop” loads, 89
+  Dwarf walls under floors, 26
+
+  Early steel girders, 68
+  Economy, 184
+  Effect of earth slips, 157
+  -- of floor on deflection, 88
+  -- -- -- on stresses, 23, 30
+  -- of high stress, 86
+  -- of permanent way on stresses, 18
+  --of skew on bridge floors, 25
+  -- -- -- on centre girders, 131
+  -- of transverse bracings, 34
+  -- of vibration on masonry, 162
+  -- of wave action on sea piers, 42
+  End bays, bottom booms, 18
+  Equilibrium of masonry arches, 162
+  Examination of bridges, 107
+  Examples of cast-iron bridges overstressed, 141
+  -- of high stress, 70
+  -- of life of bridges, 167
+  -- of rivet stress, 56
+  -- of strengthening, 114
+  -- -- -- by centre girders, 131, 134
+  Excessive bearing pressure, 51
+
+  Faulty workmanship, 80
+  Fixed ends to cross girders, 22, 118
+  Flange stresses, 63, 66, 67
+  Flanges, side loaded, 9, 73
+  Flat bar bracing, 37
+  Flexing of girders, 9, 74, 76
+  Flexure curves, 138
+  Fractured bedstones, 3
+  -- rails, 30
+  -- webs, 13, 14, 15, 50
+  Fractures in cast iron, 7, 145
+
+  Girder bearings, 2
+  Girders on columns, 7
+  -- on masonry, 8
+  Girderwork in masonry, 101
+
+  Headway, 173
+  High stress, 61
+  -- in cast iron, 141
+  -- in rivets, 47, 52
+  Holes for drainage, 25
+
+  Impact, 20, 62
+  Inclination of girder ends, 23, 53
+  Incomplete bracing, 41
+  Initial set, 88
+  Interference with traffic, 177
+
+  Jack arches, 29, 101
+  Joints in rails, 29, 109
+  -- in trough floors, 28, 180
+  Junction between metallic and masonry bridges, 183
+  -- -- new and old masonry bridges, 182
+  -- -- new and old metallic bridges, 180
+
+  Lattice girder stresses, 47-66
+  Liberal depth to girders, 23, 89, 184
+  Life of bridges, 165
+  Limit of elasticity, 61
+  Linen tapes, 172
+  Longitudinal floor girders, 23
+  Loose rivets, 21, 25, 51, 53, 56, 109
+
+  Main girders, 9-17
+  Masonry bridges, 157
+  -- enduring character of, 161
+  Memel timber, 150
+  Methods of calculation, 46, 61
+  -- of observing deflection, 90
+  -- of setting out deflection curves, 138
+  Movements of abutments, 158
+  -- of cast-iron bridge, 82
+  -- of piers, 42, 83, 159
+  -- of rollers, 7
+  -- of wrought-iron bridges, 4, 21, 38, 73
+
+  New members to old work, 116
+
+  Oiling steelwork, 99
+  Old drawings unreliable, 108
+  -- rivets, 21, 51, 54, 55
+  Open webs, 17
+  Overhead bracing, 39
+  -- girders, 118
+
+  Painting, 98
+  Parapets, 79
+  Permissible stress in old work, 110
+  Piers, movements of, 42, 83, 159
+  -- out of plumb, 159
+  Piles, decay of, 102, 150
+  Pitch pine, 28
+  Plasticity, 61
+  Plate webs, 9
+  Plated floors, 23, 25, 30
+  Pointing masonry, 164
+  Proposed rivet stresses, 58
+
+  Quickly applied loads, 89
+
+  Rail joints, 29, 109
+  Rails, breaks in, 30
+  Reaction of cross girder with centre support, 127
+  Red-lead, 98, 100
+  Relative merits of bridges, 169
+  Relief by centre girders, 122
+  Repainting, 100
+  Repair of bridges, 107, 147, 155, 163
+  -- of timber piles, 156
+  Replacing flange plates, 110
+  -- rivets, 111
+  Resistance of cast iron to rust, 101
+  Riveted connections, 45, 86
+  Rivets in cramped positions, 20
+  -- in cross girder ends, 21, 49, 53, 54
+  -- in road bridges, 60
+  -- in webs of main girders, 46
+  -- spacing of, 60, 80
+  -- stresses in, 56
+  Rocking of piers, 8, 83, 159
+  Roller bearings, 7
+  Rubble masonry, 161-164
+  Running load and deflection, 95
+  Rusting, instances of, 29, 96
+  -- of steelwork, 99
+  -- over sea-water, 98
+
+  Sag in timber bridges, 150
+  -- of tapes, 172
+  Scour under piers, 161
+  Sea piers, 42, 102
+  Setting bedstones, 3, 129, 176
+  Settlements, 76, 157
+  Skew bearings, 4
+  -- bridges, right and left, 173
+  -- -- floors, 25
+  Skirting plate, 26
+  Slope of girder ends, 92
+  Softening of cast-iron in sea-water, 101
+  Spacing of rivets, 60, 79
+  Spread of abutments, 157
+  Spring joints, 23
+  Steel trough girders, 68
+  -- troughing, 70
+  Stiffening girders from floor, 12, 40
+  -- to webs, 16, 38, 185
+  Stop piers, 158
+  Strength of light top booms, 40
+  Strengthening of bridges, 107, 122
+  -- bridge floors, 118
+  -- cross girders, 123
+  Stress in plated floors, 31
+  Study of old bridges, 185
+
+  Tall piers, 42, 159
+  Timber bridges, 149
+  -- floors, 27
+  -- staging, 177
+  Top booms, 18
+  Traffic during reconstruction, 177
+  Transverse bracing, 34, 117
+  Trough floors, 27, 180
+  -- girders, 50, 74
+  [T] stiffeners, breaks in, 16
+  Twin girders, 15, 75
+  Twisting of girders, 11, 68, 73
+  -- -- -- corrected, 12
+  Types of reconstruction, 174
+
+  [U]-shaped booms, 18
+  Uncomplicated stress, 62
+  Uniform pressure on bearings, 6
+
+  Value of E in deflection formulæ, 87
+  Vibration, 162
+
+  Wasted webs, 14, 29, 96
+  Water, scour of, 161
+  Web buckling, 16
+  -- plates, cracked, 13, 14, 15, 50
+  -- rivets, 46, 50
+  -- stiffening, 16, 38, 185
+  Widening masonry bridges, 182
+  -- metallic bridges, 179
+  Wide spaced rivets, 79
+  Wind pressure, 41, 43
+
+  Yielding of piers, 8, 83, 159
+
+
+  LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
+  GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
+
+
+
+
+Transcriber's Notes:
+
+The text of the original work (including inconsistent spelling,
+hyphenation, formatting etc.) has been retained, except as mentioned
+below.
+
+The slight differences between the Table of Contents and the text have
+not been changed.
+
+Changes made to the text:
+
+Some punctuation errors and obvious typographical errors have been
+corrected silently.
+
+Several illustrations have been moved to where they are described in the
+text.
+
+Page 123, formula (2): the original shows an unclear superscript after
+the first L. As described in the following line of the text, this has
+been changed to L{_l_}.
+
+
+
+
+
+End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
+
+*** END OF THE PROJECT GUTENBERG EBOOK 44371 ***
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+<body>
+<div>*** START OF THE PROJECT GUTENBERG EBOOK 44371 ***</div>
+
+<div class="tnbox">
+<p class="center">Please see the <a href="#TN">Transcriber&#8217;s Notes</a> at the end of this text.</p>
+</div>
+
+<hr class="chap" />
+
+<div class="noilloblock">
+<div class="figcenter">
+<img src="images/cover-b.jpg" alt="cover" width="366" height="550" />
+</div>
+<hr class="chap" />
+</div>
+
+<p><span class="pagenum"><a name="Page_v" id="Page_v"></a></span></p>
+<h1>THE<br />
+ANATOMY OF BRIDGEWORK</h1>
+
+<hr class="chap" />
+
+<p class="center highline blankabove"><span class="fsize125">THE</span><br />
+<span class="fsize175">ANATOMY OF BRIDGEWORK</span></p>
+
+<p class="center highline">BY</p>
+
+<p class="center blankabove"><span class="fsize150">WILLIAM HENRY THORPE</span><br />
+ASSOC. M. INST. C. E.</p>
+
+<p class="center highline blankabove blankbelow sstype">WITH 103 ILLUSTRATIONS</p>
+
+<div class="figcenter">
+<img src="images/illo003.png" alt="logo" width="150" height="176" />
+</div>
+
+<p class="center blankabove"><span class="oldtype">London</span><br />
+E. &amp; F. N. SPON, <span class="smcap">Limited</span>, 57 HAYMARKET<br />
+<span class="oldtype">New York</span><br />
+SPON &amp; CHAMBERLAIN, 123 LIBERTY STREET<br />
+1906</p>
+
+<hr class="chap" />
+
+<h2>PREFACE</h2>
+
+<p>In offering this little book to the reader interested in
+Bridgework, the author desires to express his acknowledgments
+to the proprietors of &#8220;Engineering,&#8221; in which journal
+the papers first appeared, for their courtesy in facilitating
+the production in book form.</p>
+
+<p>It may possibly happen that the scanning of these pages
+will induce others to observe and collect information extending
+our knowledge of this subject&mdash;information which,
+while familiar to maintenance engineers of experience, has
+not been so readily available as is desirable.</p>
+
+<p>No theory which fails to stand the test of practical
+working can maintain its claims to regard; the study of
+the behaviour of old work has, therefore, a high educational
+value, and tends to the occasional correction of views which
+might otherwise be complacently retained.</p>
+
+<p><span class="padl2">60 <span class="smcap">Winsham Street</span>,</span><br />
+<span class="padl4"><span class="smcap">Clapham Common, London, S.W.</span></span><br />
+<span class="padl6"><i>October</i>, 1906.</span></p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_vi" id="Page_vi"></a><br /><a name="Page_vii" id="Page_vii">[vii]</a></span></p>
+
+<h2>CONTENTS</h2>
+
+<table class="toc" summary="ToC">
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER I.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">INTRODUCTION&mdash;GIRDER BEARINGS.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="right fsize80">PAGE</td>
+</tr>
+
+<tr>
+<td class="subjects">Pressure distribution&mdash;Square and skew bearings&mdash;Fixed bearings&mdash;Knuckles&mdash;Rollers&mdash;Yield of supports</td>
+<td class="pagenr"><a href="#Page_1">1</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER II.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">MAIN GIRDERS.</td>
+</tr>
+
+<tr>
+<td class="subjects"><i>Plate webs</i>: Improper loading of flanges&mdash;Twisting of girders&mdash;Remedial measures&mdash;Cracks in webs&mdash;Stiffening of webs&mdash;<span class="lettsymb">T</span> stiffeners</td>
+<td class="pagenr"><a href="#Page_9">9</a></td>
+</tr>
+
+<tr>
+<td class="subjects"><i>Open webs</i>: Common faults&mdash;Top booms&mdash;Buckling of bottom booms&mdash;Counterbracing&mdash;Flat members</td>
+<td class="pagenr"><a href="#Page_17">17</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER III.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">BRIDGE FLOORS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Liability to defects&mdash;Impact&mdash;Ends of cross and longitudinal girders&mdash;Awkward riveting&mdash;Fixed ends to cross girders&mdash;Plated floor&mdash;Liberal depths desirable&mdash;Type connections&mdash;Effect of &#8220;skew&#8221; on floor&mdash;Water-tightness&mdash;Drainage&mdash;Timber floors&mdash;Jack arches&mdash;Corrugated sheeting&mdash;Ballast&mdash;Rail joints&mdash;Effect of main girders on floors</td>
+<td class="pagenr"><a href="#Page_20">20</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER IV.<span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">BRACING.</td>
+</tr>
+
+<tr>
+<td class="subjects">Effect of bracing on girders&mdash;Influence of skew on bracing&mdash;Flat bars&mdash;Overhead girders&mdash;Main girders stiffened from floor&mdash;Stiffening of light girders&mdash;Incomplete bracing&mdash;Tall piers&mdash;Sea piers</td>
+<td class="pagenr"><a href="#Page_34">34</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER V.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">RIVETED CONNECTIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Latitude in practice&mdash;Laboratory experiments&mdash;Care in considering practical instances&mdash;Main girder web rivets&mdash;Lattice girders investigated&mdash;Rivets in small girders&mdash;Faulty bridge floor&mdash;Stresses in rivets&mdash;Cross girder connections&mdash;Tension in rivets&mdash;Defective rivets&mdash;Loose rivets&mdash;Table of actual rivet stresses&mdash;Bearing pressure&mdash;Permissible stresses&mdash;Proposed table&mdash;Immunity of road bridges from loose rivets&mdash;Rivet spacing</td>
+<td class="pagenr"><a href="#Page_45">45</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VI.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">HIGH STRESS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Elastic limit&mdash;Care in calculation&mdash;Impact&mdash;Examples of high stress&mdash;Early examples of high stress in steel girders&mdash;Tabulated examples&mdash;General remarks</td>
+<td class="pagenr"><a href="#Page_61">61</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DEFORMATIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Various kinds&mdash;Flexing of girder flanges&mdash;Examples&mdash;Settlement deformations&mdash;Creeping&mdash;Temperature changes&mdash;Local distortions&mdash;Imperfect workmanship&mdash;Deformation of cast-iron arches</td>
+<td class="pagenr"><a href="#Page_73">73</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VIII.<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DEFLECTIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Differences as between new work and old&mdash;Influence of booms and web structure on deflection&mdash;Yield of rivets and stiffness of connections&mdash;Working formul&aelig;&mdash;Set&mdash;Effect of floor system&mdash;Deflection diagrams&mdash;Loads quickly applied&mdash;&#8220;Drop&#8221; loads&mdash;Flexible girders&mdash;Measuring deflections&mdash;New method of observing deflections&mdash;Effect of running load</td>
+<td class="pagenr"><a href="#Page_85">85</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER IX.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DECAY AND PAINTING.</td>
+</tr>
+
+<tr>
+<td class="subjects">Examples of rusting of wrought-iron girders&mdash;Girder over sea-water&mdash;Rate of rusting&mdash;Steelwork&mdash;Precautions&mdash;Red-lead&mdash;Repainting&mdash;Scraping&mdash;Girders built into masonry&mdash;Cast iron&mdash;Effect of sea-water on cast iron&mdash;Examples&mdash;Tabulated observations&mdash;Percentage of submersion&mdash;Quality of metal</td>
+<td class="pagenr"><a href="#Page_96">96</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER X.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Purpose&mdash;Methods of examination&mdash;Calculations&mdash;Stress in old work&mdash;Methods of reducing stress&mdash;Repair&mdash;Loose rivets&mdash;Replacing wasted flange plates&mdash;Adding new to old sections&mdash;Principles governing additions&mdash;Example&mdash;Strengthening lattice girder bracings&mdash;Bracing between girders&mdash;Strengthening floors&mdash;Distributing girders</td>
+<td class="pagenr"><a href="#Page_107">107</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XI.<span class="pagenum"><a name="Page_x" id="Page_x">[x]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Principal methods in use&mdash;Method of calculation&mdash;Adjustments&mdash;Connections&mdash;Method of execution&mdash;Checks&mdash;Effect of skew on method considered&mdash;Results of calculation for a typical case&mdash;Probable error&mdash;Practical examples&mdash;Special case&mdash;Method of determining flexure curves</td>
+<td class="pagenr"><a href="#Page_122">122</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">CAST-IRON BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Limitations of cast iron&mdash;Stress examples&mdash;Advantages and disadvantages&mdash;Foundry stresses&mdash;Examples&mdash;Want of ductility of cast iron&mdash;Repairs&mdash;Restricted possibilities</td>
+<td class="pagenr"><a href="#Page_141">141</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XIII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">TIMBER BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Perishable nature&mdash;Causes of decay&mdash;Sag&mdash;Lateral bracing&mdash;Piles&mdash;Uncertainty respecting decay&mdash;Examples&mdash;Conditions and practice favourable to durability&mdash;Bracing&mdash;Protection&mdash;Repair&mdash;Piles&mdash;Cost</td>
+<td class="pagenr"><a href="#Page_149">149</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XIV.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">MASONRY BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Definition&mdash;Cause of defects or failure&mdash;Spreading of abutments&mdash;Closing in&mdash;Example&mdash;Stop piers&mdash;Example of failure&mdash;Strength of rubble arch&mdash;Equilibrium of arches&mdash;Effect of vibration on masonry&mdash;Safety centring&mdash;Methods of repair&mdash;Pointing&mdash;Rough dressed stonework</td>
+<td class="pagenr"><a href="#Page_157">157</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XV.<span class="pagenum"><a name="Page_xi" id="Page_xi">[xi]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">LIFE OF BRIDGES&mdash;RELATIVE MERITS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Previous history&mdash;Causes of limited life&mdash;Tabulated examples of short-lived metallic bridges&mdash;Timber and masonry bridges&mdash;Durability&mdash;Maintenance charges&mdash;First cost&mdash;Comparative merits&mdash;Choice of material</td>
+<td class="pagenr"><a href="#Page_165">165</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XVI.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">RECONSTRUCTION AND WIDENING OF BRIDGES.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">CONCLUSION.</td>
+</tr>
+
+<tr>
+<td class="subjects">Measuring up&mdash;Railway under-bridges&mdash;Methods of reconstruction in common use&mdash;Reconstruction of bridges of many openings&mdash;Timber staging&mdash;Traffic arrangements&mdash;Sunday work&mdash;Railway over-bridges&mdash;Widenings&mdash;Junction of new and old work&mdash;Concluding remarks&mdash;Study of old bridgework</td>
+<td class="pagenr"><a href="#Page_172">172</a></td>
+</tr>
+
+<tr>
+<td class="left blankabove">INDEX</td>
+<td class="pagenr"><a href="#Page_187">187</a></td>
+</tr>
+
+</table>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p>
+
+<p class="center highline blankabove blankbelow"><b><span class="fsize125">THE</span><br />
+<span class="fsize175">ANATOMY OF BRIDGEWORK.</span></b></p>
+
+<hr class="chap" />
+
+<h2>CHAPTER I.<br />
+<span class="chaptitle">INTRODUCTION.</span></h2>
+
+<p>No book has, so far as the author is aware, been written
+upon that aspect of bridgework to be treated in the following
+pages. No excuse need, therefore, be given for adding to
+the already large amount of published matter dealing with
+bridges. Indeed, as it too often happens that the designing
+of such constructions, and their after-maintenance, are in
+this country entirely separated, it cannot but be useful to
+give such results of the behaviour of bridges, whether new
+or old, as have come under observation.</p>
+
+<p>In the early days of metallic bridges there was of necessity
+no experience available to guide the engineer in his
+endeavour to avoid objectionable features in design, and he
+was, as a result, compelled to rely upon his own foresight
+and judgment in any attempt to anticipate the effects of
+those influences to which his work might later be subject.
+How heavily handicapped he must have been under these
+conditions is evident from the mass of information since
+acquired by the experimental study of the behaviour of
+metals under stress, and the growth of the literature of
+bridgework during the last forty years. That many mistakes
+were made is little occasion for surprise; rather is it a cause<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span>
+for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the
+study of defects and failures, even though they be of such a
+character that no experienced designer would now furnish
+like examples.</p>
+
+<p>Modern instances may, none the less, be found, with
+faults repeated, which should long since have disappeared
+from all bridgework, and are only to be accounted for by
+the unnatural divorce of design and maintenance already
+referred to. As the reader proceeds, it may appear that
+details are occasionally touched upon of a character altogether
+too crude and objectionable to need comment; but the
+consideration of these cases is none the less interesting, and,
+so far as the author&#8217;s observation goes, not altogether unnecessary.</p>
+
+<p>Most of the instances cited are of bridges, or parts of
+bridges, of quite small dimensions; but it is these which
+most commonly give trouble, both because the effects of impact
+are in such cases most severely felt, and possibly because
+the smaller class of bridges is very generally designed by men
+of less experience, than large and imposing structures.</p>
+
+<p>The particulars given relate in all cases to bridges of
+wrought iron, unless otherwise described.</p>
+
+<p>An endeavour has been made to secure some kind of
+order in dealing with the subject, but it has been found
+difficult to avoid a somewhat disjointed treatment, inseparable,
+perhaps, from the nature of the matter. Finally,
+the reader may be assured that every case quoted has come
+under the writer&#8217;s personal notice.</p>
+
+<h3><span class="smcap">Girder Bearings.</span></h3>
+
+<p>In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing
+allowed. Clearly, the surface over which the pressure<span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span>
+is distributed should be sufficiently ample to avoid overloading
+and possible crushing or fracture of bedstones where
+these exist; but if no knuckles are introduced, this is an
+extremely difficult matter to insure. A long bearing may
+deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.</p>
+
+<p>If the girder is made with truly level bearings, and the
+beds set level, it will certainly, when under load, throw an
+extreme pressure upon that part of the bearing surface
+immediately under the forward edge of the bearing-plate.
+These considerations probably account for bedstones frequently
+cracking, in addition to which possibility there is
+the disadvantage that the designer does not know where the
+girder will rest, and cannot truly define the span. The
+variation of flange-stress due to this cause may, in a girder
+of ordinary proportions, having bearings equal in length to
+the girder&#8217;s depth, be as much as 15 per cent. above or
+below that intended.</p>
+
+<p>If great care be taken in setting beds, in the first instance,
+to dip toward the centre of the span an amount depending
+upon the anticipated girder deflection, it may be possible to
+insure that when under full load the girder bearing shall
+rest equally upon its seat; but this is evidently a difficult
+condition to obtain practically, is good only for one degree of
+loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence
+of a slight leaning forward of abutment walls.</p>
+
+<p>Double or treble thicknesses of hair-felt are sometimes
+placed beneath girder bearings, with the object of securing
+a better distribution of pressure, no doubt with advantage;
+but this practice, though it may be quite satisfactory as
+applied to girders carrying an unchangeable load, hardly
+meets the case for loads which are variable. Notwithstanding
+the faulty nature of the plain bearing ordinarily used<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span>
+for girders of moderate span, its extreme simplicity commends
+it to most engineers. It must be admitted that no serious
+inconvenience need be anticipated in the majority of cases,
+particularly if the bearings are limited in length, do not
+approach nearer than 3 inches to the face of bedstones, and
+are furnished with hair-felt or similar packing.</p>
+
+<div class="figcenter"><a name="Fig1" id="Fig1"></a>
+<img src="images/illo016.png" alt="" width="450" height="216" />
+<p class="caption"><span class="smcap">Fig.</span> 1.</p>
+</div>
+
+<p>Whether with long or short bearings, the forward edge
+should be at right angles to the girder&#8217;s length. In skew
+bridges it is sometimes seen that this edge follows the angle
+of skew. The effect on the girder is to twist it, as will be
+clear from a little consideration. In evidence of this the
+case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment
+right up to the masonry face at a rather bad angle (about
+15 degrees), was, after twenty years, found canted over at
+the top to the extent of 4 inches, with the further result of
+springing a joint in the top flange at about the middle of
+the girder, causing some rivets to loosen. The bedstone
+was also very badly broken at the face, and had to be
+replaced in the course of repairs (<a href="#Fig1">Fig. 1</a>). This girder had,
+in addition to the canting from the upright position at its
+end, and the distortion of the top flange, a curvature in the
+same direction, though less in amount, at the bottom&mdash;an<span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span>
+effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder
+end to creep along the abutment away from the point at
+which it bears hardest, under frequent applications and
+removals of the live load, and accompanying deflections.</p>
+
+<p>This tendency to travel may be aggravated in bridges
+carrying a ballasted road, in which there may be a considerable
+thickness of ballast near the bearings, by the compacting
+and spreading of this material taking effect upon the
+girder end, tending to push it outwards, being tied only by
+a few light cross-girders badly placed for useful effect.
+The movement may be prevented in new work for moderate
+angles of skew by carrying the end cross-girders well back,
+and securing them in some efficient manner; or by the
+introduction of a diagonal tie following the skew face, and
+attached to cross and main girder flanges (<a href="#Fig2">Fig. 2</a>)&mdash;a method
+which may be applied to existing work also.</p>
+
+<div class="figcenter"><a name="Fig2" id="Fig2"></a>
+<img src="images/illo017.png" alt="" width="350" height="232" />
+<p class="caption"><span class="smcap">Fig.</span> 2.</p>
+</div>
+
+<p>For such a case as that cited it is imperative that ballast
+pressure at the girder end should be altogether eliminated.</p>
+
+<p>The fixing of girder ends by bolts&mdash;a practice at one
+time usual&mdash;hardly calls for remark, as it is now seldom
+resorted to unless for special reasons; but it may be well to
+point out the weakening effect of holes for any purpose in<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span>
+bedstones. Bed-plates commonly need no fixing; the weight
+carried keeps them in position, or if, in the case of very
+light girders upon separate plates, it is considered well to
+secure these from shifting, it may best be done by letting
+the plate in bodily a small amount, or by means of a very
+shallow feather sunk into a chase.</p>
+
+<div class="figcenter"><a name="Fig3" id="Fig3"></a>
+<img src="images/illo018.png" alt="" width="450" height="298" />
+<p class="caption"><span class="smcap">Fig.</span> 3.</p>
+</div>
+
+<p>As an improvement upon the plain bearing usually
+adopted, it is an easy matter so to design girder-ends as to
+deliver the load by a narrow strip of bearing-plate carried
+across the bottom flange, distributing the pressure upon the
+stone, if there be one, by means of a simple rectangular plate
+of sufficient stoutness (<a href="#Fig3">Fig. 3</a>). An imperfect knuckle will
+by this means result, with freedom to slide, and the girder
+span be defined within narrow limits. A true knuckle is, of
+course, the best means of securing imposition of the load
+always in the same place; but this by itself is not sufficient
+where the girder is of a length to make temperature and
+stress variations important, in which case rollers, or freedom
+to slide, become necessary. Bridges exist in which roller-bearings
+have been adopted without the knuckle, or its<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span>
+equivalent, but this is wholly indefensible, as it is obvious
+that the forward roller will in all probability take the whole
+load, and cannot be expected to keep its shape and roll freely
+under this mal-treatment. It is sometimes asserted that
+rollers are never effective after some years&#8217; use; that they
+become clogged with dirt, and refuse to perform their office.</p>
+
+<p>There is no reason why rollers should not be boxed in to
+exclude dirt by a casing easily removed, some attention being
+given to them, and any possible accumulation of dirt removed
+each time the bridge is painted.</p>
+
+<p>To test the behaviour of rollers under somewhat unfavourable
+conditions for their proper action&mdash;that of the
+bearings of main roof trusses of crescent form, 190 feet span&mdash;the
+author, some thirty years since, took occasion to make
+the necessary observations, and found evidence of a moderate
+roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders
+resting upon columns, particularly if of cast iron, a roller
+and knuckle arrangement is most desirable for any but very
+small spans, as, if not adopted, the result will be a canting
+of the columns from side to side&mdash;a very small amount, it is
+true, but sufficient to throw the load upon the extreme edges
+of the base, though the knuckle alone will relieve the top of
+this danger. The author at one time took the trouble to
+examine, so far as it could be done superficially and without
+opening out the ground to make a complete inspection
+possible, a number of bridges crossing streets, in which
+girders rested upon and were secured to cast-iron columns
+standing in the line of kerb; and he found cracks, either at
+the top or bottom, in about one of every four columns.</p>
+
+<p>When girders passing over columns are not continuous,
+it may be difficult to find room for a double roller and
+knuckle arrangement; but this inconvenience may be overcome
+by carrying one girder-end wholly across the column-top,<span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span>
+and securing the next girder-end to it in a manner
+which a little care and ingenuity will render satisfactory,
+one free bearing then serving to carry the load from both
+girders.</p>
+
+<p>Though the wisdom of using rollers is apparent in spans
+exceeding some moderate length, say 80 feet&mdash;as to which
+engineers do not seem quite decided&mdash;and varying with the
+conditions, it need not be overlooked that in some cases
+masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will
+yield a small amount without injury, and though shorter, if
+resting upon a bottom not absolutely rigid, will rock and
+give the necessary relief; but it is obvious, if the resistance
+to movement is sufficiently great, and the girder cannot slide
+or roll on its bearings, bedstones will probably loosen, as,
+indeed, frequently happens.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span></p>
+
+<h2>CHAPTER II.<br />
+<span class="chaptitle">MAIN GIRDERS; PLATE-WEBS.</span></h2>
+
+<p>It is seldom that girders of this description&mdash;or, indeed, of
+any other&mdash;show signs of failure from mere defect of strength
+in the principal parts, even though somewhat highly stressed;
+and instances tending to support this statement will be given
+in a later chapter. For the present, it is proposed to indicate
+peculiarities of behaviour only, generally, but not always,
+harmless.</p>
+
+<p>Though now less often done, it was at one time common
+practice to load plate-girders on the bottom flange by simply
+resting floor timbers, rails, troughs, or cross-girders upon
+them. In outside girders one result of this is to cause the
+top flange to take a curve in plan, convex towards the road,
+every time the live load comes upon the floor of the bridge,
+upon the passing of which the flange resumes its figure, though
+still affected by that part of the load which is constant.</p>
+
+<p>A bridge of 47 feet span, carrying two lines of way,
+having one centre and two outside girders, with a floor consisting
+of old Barlow rails, resting upon the bottom flanges,
+showed the peculiarity named in a marked degree.</p>
+
+<p>The outside girders, under dead load only, were, as to
+the top flanges (see <a href="#Fig4">Figs. 4</a> and <a href="#Fig5">5</a>), 1<sup>1</sup>&#8260;<sub>4</sub> inch and 1<sup>1</sup>&#8260;<sub>16</sub> inch
+respectively out of straight in their length, but upon the
+passing of a goods engine and train curved an additional 1<sup>1</sup>&#8260;<sub>8</sub>
+inch, or 2<sup>3</sup>&#8260;<sub>8</sub> inches in all, for one outside girder, and 2<sup>3</sup>&#8260;<sub>16</sub>
+inches for the other.</p>
+
+<p>The centre girder, having a broader and heavier top<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span>
+flange, curved <sup>5</sup>&#8260;<sub>8</sub> inch towards whichever road might be
+loaded. The effect of such horizontal
+flexure is clearly to induce stresses of
+tension and compression in the flanges,
+which, being (for the top flange) compounded
+with the normal compressive
+stress due to load carried, results in a
+considerable want of uniformity across
+the section.</p>
+
+<div class="figcenter"><a name="Fig4" id="Fig4"></a>
+<img src="images/illo022.png" alt="" width="600" height="149" />
+<p class="caption"><span class="smcap">Fig.</span> 4.</p>
+</div>
+
+<p>In the case under notice, the writer
+estimates the stresses for an outer
+girder top flange at 4&middot;5 tons per
+square inch compression for simple
+loading, and 5&middot;5 tons per square inch
+of tension and compression, on the
+inner and outer edges, due to flexure,
+resulting when compounded in a stress
+of 1 ton per square inch tension on
+the inside, and 10 tons per square inch
+compression on the outside edge. In
+this rather extreme case the stress on
+the inner edge, or that nearest the
+load, is reversed in character.</p>
+
+<p>The effect described appears to be
+not wholly due to the twisting moment.
+It is apparent that whatever curvature
+may be induced by twisting alone
+must be aggravated in the compression
+flange by its being put out of line.</p>
+
+<p>The writer does not attempt here to
+apportion the two effects in any other
+way than to say that the greater part
+of the flexure appears to be due to the secondary cause. Consistent
+with this view of the matter is the fact that the inclination<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span>
+of the girder towards the rails greatly exceeded the
+calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the
+floor rails bore hard at their extreme ends, at which point of
+bearing the calculated twisting moment accounts for less
+than one-half of the flexure observed in the flanges.</p>
+
+<div class="figcenter"><a name="Fig5" id="Fig5"></a>
+<img src="images/illo023.png" alt="" width="400" height="321" />
+<p class="caption"><span class="smcap">Fig.</span> 5.</p>
+</div>
+
+<p>The girders upon removal in the course of reconstruction
+again took the straight form, showing that the very
+frequent development of the stresses named had not sensibly
+injured the metal, though the bridge carried as many as
+three hundred trains daily in each direction, and had done so
+for very many years.</p>
+
+<p>The deformation of the top flange only has been noticed,
+yet the same tendency exists in the bottom, though the actual
+amount is much less, both because the lower flanges are in
+tension, and are also in great degree confined by the frictional
+contact of the cross bearers, even where no proper ties
+are used. In the case dealt with the bottom flanges of
+the outer girders curved <sup>1</sup>&#8260;<sub>8</sub> inch outwards only.</p>
+
+<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p>
+
+<p>With the broad flanges commonly adopted in English
+practice, twisting of the girders, under conditions similar to
+the above, will not generally be a serious matter; but with
+narrow flanges possessing little lateral stiffness it might be a
+source of danger.</p>
+
+<div class="figc450"><a name="Fig6" id="Fig6"></a><a name="Fig7" id="Fig7"></a>
+<img src="images/illo024.png" alt="" width="450" height="282" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 6.</span>
+<span class="right49"><span class="smcap">Fig.</span> 7.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 6. and <span class="smcap">Fig.</span> 7.</p>
+</div>
+
+<p>The twisting may be limited in amount by introducing
+a cross-frame between the girders, from which they are
+stiffened; by strutting the girders immediately from the floor
+itself, in which case they cannot cant to a greater extent
+than that which corresponds to the floor deflection; or by
+designing the top flange to be unsymmetrical with reference
+to the web, as in <a href="#Fig6">Figs. 6 and 7</a>, with the object of insuring
+that under the joint effect of vertical loading and twisting,
+the stress in the flange shall at maximum loads be uniform
+across the section, and allow it to remain straight. This
+may be secured by making the eccentricity of the flange
+section equal to that of the loading. For instance, if the load
+be applied 3 inches away from the web centre, the flange
+should have its centre of gravity 3 inches on the other side
+of the centre line. It can be shown that this is true
+throughout the length of the girder, and irrespective of the
+depth. An instance in which flange eccentricity being in
+excess, curvature outwards resulted, will be found in a later<span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span>
+chapter on deformations, etc. It will not generally be
+necessary to make the bottom flange eccentric, as it is
+commonly tied in some way; but if done, the eccentricity
+should be on the same side as for the top. The flanges
+remaining straight under these conditions are not subject to
+the complications of stress referred to in the case first quoted.
+The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the
+kind discussed.</p>
+
+<p>It should be remarked that by the two first methods, if
+the stiffening frames are wide apart and attached direct to
+the web, there is a liability for this to tear, under distress,
+rather than keep the girder in line.</p>
+
+<p>There is one other possible consequence of throwing load
+upon the flanges of a girder of a much more alarming nature.
+In girders not very well stiffened, it may happen that the
+frequent application of load in this manner finally so injures
+the web-plate, just above the top edge of the bottom angle-bars,
+as to cause it to rip in a horizontal direction. More
+likely is this to happen with a centre girder taking load first
+on one side, then on the other, and again on both together.
+Cases may be cited in which cracks right through the webs
+3 feet or more in length have resulted from this cause. It
+is very probable, however, that in some of these cases the
+matter was aggravated by the use of a poor iron in the webs,
+as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a
+girder, would, if they could not be made thin enough, even
+encourage the use of an indifferent metal as being quite good
+enough for that part of the work.</p>
+
+<p>An instance of web-fracture from somewhat similar causes
+may be here given.</p>
+
+<p>In a bridge of 31 feet 6 inches effective span, and consisting
+of twin girders carrying rails between, as shown in <a href="#Fig8">Figs.
+8</a> and <a href="#Fig9">9</a>, the load resting upon the inner ledges, formed by<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span>
+the bottom flange, induced such a bending and tearing action
+along the web just above the angle-bars,
+as to cause a rip in one of the girders, well
+open for some distance, and which could
+be traced for 14 feet as a continuous crack.</p>
+
+<div class="figcenter"><a name="Fig8" id="Fig8"></a>
+<img src="images/illo026.png" alt="" width="600" height="101" />
+<p class="caption"><span class="smcap">Fig.</span> 8.</p>
+</div>
+
+<div class="figcenter"><a name="Fig9" id="Fig9"></a>
+<img src="images/illo027.png" alt="" width="450" height="309" />
+<p class="caption"><span class="smcap">Fig.</span> 9.</p>
+</div>
+
+<p>It will be noticed in the figure that the
+<span class="lettsymb">T</span> stiffeners occur only at the outer face of
+the web, and that the inner vertical strips
+stop short at the top edge of the angles,
+the result being that under load the flange
+would tend to twist around some point, say
+A, at each stiffener, inducing a serious stress
+in the thin web at that place, while away
+from these stiffeners the web would be
+more free to yield without tearing. The
+fact that at a number of the stiffeners
+incipient cracks were observed, some only
+a few inches long, suggests this view of
+the matter.</p>
+
+<p>A case of web-failure from other influences
+coming under notice showed breaks
+at the upper part of the web extending
+downwards.</p>
+
+<p>In this bridge, of 32 feet span, which
+had been in existence thirty-two years,
+the webs&mdash;originally <sup>1</sup>&#8260;<sub>4</sub> inch thick&mdash;were,
+largely because of cinder ballast in contact
+with them, so badly wasted as to be generally
+little thicker than a crown-piece, and
+in places were eaten through; in addition
+to which, the road being on a sharp curve,
+the rail-balks had been strutted from the
+webs to keep them in position, the effect
+of which would be to exert a hammering thrust upon the<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span>
+face of the web at the abutting ends, and assist in starting
+cracks in webs already much corroded. A feature of this case,
+tending to show that the breaks resulted as the joint effect of
+waste and ill-usage by the strut members, rather than by excessive
+stress in the web as reduced, is to be found in the fact that
+the girders when removed were observed to be in remarkably
+good shape&mdash;i.e. the camber, marked on the original drawings
+to be 1<sup>1</sup>&#8260;<sub>2</sub> inch, still showed as a perfectly even curve of that
+rise, which would hardly have been the case if the lower
+flange had been let down by web-rupture, the result of
+excessive web-stresses.</p>
+
+<p>Occasionally webs will crack through the solid unwasted
+plate, in a line nearly vertical; not where shear stress is
+greatest, but generally at some other place, and from no
+apparent cause, either of stress or ill-usage. The writer has
+observed this only in the case of small girders not exceeding
+2 feet in depth; and, for want of any better reason, attributes
+these cracks to poor material, coupled with some latent defect.
+In a bridge having some thirty cross-girders, each 26 feet
+long, about every other one had a web cracked in this
+manner after many years&#8217; use.</p>
+
+<p><span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span></p>
+
+<p>Web-cracks of the kind first indicated, are perhaps, the
+most probable source of danger in plate-girders, of any which
+are likely to occur. The fault is insidious, difficult to detect
+when first developed, and perhaps not seen at all till the
+bridge, condemned for some other reason, has the girders
+freely exposed and brought into broad light. The manner
+in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of
+these defects an uncertain matter, unless sufficient trouble is
+occasionally taken to render inspection complete.</p>
+
+<p>The manner in which girders with wasted and fractured
+webs will still hang together under heavy loading seems to
+warrant the deduction that, in designing new work, it can
+hardly be necessary to provide such a considerable amount of
+web-stiffening as is sometimes seen; experience showing that
+defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form
+of cracks.</p>
+
+<p>A case of web-buckling lies, so far, without the author&#8217;s
+experience. There is no need to introduce, for web-stresses
+alone, more stiffening than that which corresponds to making
+the stiffeners do duty as vertical struts in an openwork
+girder; in which case it is sufficient to insure that the
+stiffeners occurring in a length equal to the girder&#8217;s depth
+shall, as struts, be strong enough in the aggregate to take
+the whole shear force at the section considered, in no case
+exceeding this amount on one stiffener. For thin webs in
+which the free breadth is greater than one hundred and
+twenty times the thickness, the diagonal compressive stress
+may be completely ignored, and the thickness determined
+with reference to the diagonal tension stress only.</p>
+
+<p>There is one fault which frequently shows itself in
+stiffeners though not the result of web-stresses, and when
+performing an additional function&mdash;viz., the breaking of<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span>
+<span class="lettsymb">T</span> stiffener knees at the weld, where brought down on to the
+tops of cross-girders, due to the deflection of the floor, as
+shown in <a href="#Fig10">Fig. 10</a>. When such knees are used, the angle
+may properly be filled in with a gusset-plate to relieve the
+weld of strain and prevent fracture.</p>
+
+<div class="figcenter"><a name="Fig10" id="Fig10"></a>
+<img src="images/illo029.png" alt="" width="350" height="343" />
+<p class="caption"><span class="smcap">Fig.</span> 10.</p>
+</div>
+
+<p>There is some little temptation in practice to make use
+of the solid web as a convenient stop for ballast, or road
+material. Special means, perhaps at the cost of some little
+trouble, should be adopted, where necessary, to avoid this.</p>
+
+<h3><span class="smcap">Main Girders; Open Webs.</span></h3>
+
+<p>With these, as with plate-girders, deficiency of strength&mdash;i.e.
+of section strength&mdash;is seldom so marked as to be a
+reasonable cause of anxiety. In particular instances faults
+in design may result in stresses of an abnormal amount,
+though rarely to an extent occasioning any ill effects. The
+practice of loading the bottom flanges at a distance from<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span>
+the centre, the bad effects of which have already been dealt
+with as applied to plate-girders, is not commonly resorted to
+in girders having open webs, nor are these so liable to be
+heaped with ballast in immediate proximity to essential
+members of the structure.</p>
+
+<p>Some defects are, however, occasionally seen which may
+be remarked. Top booms of an inverted <span class="lettsymb">U</span> section are
+sometimes made with side webs too thin, and having the
+lower edges stiffened insufficiently, or not at all. Where
+this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to
+sustain the compressive stress to which the rest of the boom
+is liable. The practice of putting the greater part of the
+boom section in an outer flange, characteristic of this defect,
+has the further disadvantage of throwing the centre of gravity
+of the section so near its outer edge as to make impracticable
+the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section
+is thrown into the flange-plates, the centre of gravity of the
+section has no constant position along the boom&mdash;an additional
+inconvenience where correct design is aimed at.</p>
+
+<p>These considerations indicate the propriety of arranging
+the bulk, or all, of the section at the sides, thus reducing or
+getting rid of the objections named.</p>
+
+<p>Where the bottom boom consists of side plates, only one
+point demands attention. It is found that, though nominally
+in tension, the end bays are liable occasionally to buckle, as
+though under compressive stress, and need stiffening, not
+excepting girders which at one end are mounted on rollers.
+This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes,
+such as wind forces, or as in the case of a bridge carrying a
+railway, in which the rigidity of the permanent-way may be
+such that the bridge-structure, in extending towards the<span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span>
+roller end, cannot move it sufficiently, causing a reversal of
+stress on the lighter portions of the bottom boom at the
+knuckle end; or by the exposed girder booms becoming
+very sensibly hotter than the bridge floor, and by expanding
+at a greater rate, cause this effect, from which rollers cannot
+protect them.</p>
+
+<p>In counterbracing consisting of flat bars it is desirable
+either to secure these where they cross other members, or
+stiffen them in some manner to avoid the disagreeable
+chattering which will otherwise commonly be found to occur
+on the passage of the live load.</p>
+
+<p>Occasionally diagonal ties are made up of two flat bars
+placed face to face, to escape the use of one very thick
+member. Where this is done, the two thicknesses, if not
+riveted together along the edges, will be liable to open, as
+the result of rusting between the bars in contact, when the
+evil will be aggravated by the greater freedom with which
+moisture will enter the space.</p>
+
+<p>Other matters relating to open-web girders will be more
+conveniently dealt with under their separate headings, particularly
+a further consideration of the relationship subsisting
+between the booms and floor structure.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span></p>
+
+<h2>CHAPTER III.<br />
+<span class="chaptitle">BRIDGE FLOORS.</span></h2>
+
+<p>The floors of bridges commonly give more trouble in maintenance,
+and their defects are more frequently the cause
+which renders reconstruction necessary, apart from reasons
+not concerning strength, than any other part of such structures.
+When it is considered that this portion of a bridge
+is first affected by impact of the load which comes upon it,
+and is usually light in comparison with the main girders
+further removed from the load, and to which the latter is
+transferred through the more or less elastic floor, the fact
+will be readily appreciated by those not already familiar
+with it.</p>
+
+<p>The end attachments of cross and longitudinal girders
+are very liable to suffer by loosening of rivets, or, more
+rarely, by breaking of the angle-irons which commonly make
+such a connection. A not unusual defect of old work, which
+may also sometimes be seen in work quite new, where the
+cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends.
+There is small chance of these ever being properly tight, if
+the act of riveting is rendered difficult by bad design. This
+is the more objectionable if it happens that cross-girder ends
+abut against opposite sides of the web of an intermediate
+main girder, and are secured by the same rivets passing
+through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which
+they become subject, as the cross-girders take their load and<span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span>
+deflect under it, will be very apt to loosen them. The author
+has seen a case of this kind (see <a href="#Fig11">Figs. 11</a> and <a href="#Fig12">12</a>)&mdash;rather
+extreme, it is true&mdash;in which nearly the whole of the cross-girder
+end rivets were loose, some nearly worn through, thus
+allowing the cross-girders to be carried, not by their attachments,
+but by resting upon the main-girder flanges, which
+in turn, by repeated twisting, tore the web for a length of
+4 feet; there was also pronounced side flexure of the top
+booms. The movements generally on this bridge (of 42-feet
+span), whether of main or cross-girders, were very considerable
+and disturbing. It was removed after about twenty-three
+years&#8217; use.</p>
+
+<div class="figcenter"><a name="Fig11" id="Fig11"></a>
+<img src="images/illo033a.png" alt="" width="400" height="259" />
+<p class="caption"><span class="smcap">Fig.</span> 11.</p>
+</div>
+
+<div class="figcenter"><a name="Fig12" id="Fig12"></a>
+<img src="images/illo033b.png" alt="" width="400" height="96" />
+<p class="caption"><span class="smcap">Fig.</span> 12.</p>
+</div>
+
+<p>There is no necessity, as a rule, for the ends of cross-girders
+attached to the same main girder at opposite sides
+to be placed in line. The author prefers to arrange them to
+miss, by which device each connection is entirely separate,<span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span>
+the riveting can be more efficiently executed, erection is
+simplified, and the rivets will be more likely to keep tight.
+Other special cases of cross-girder ends will be dealt with
+under the head &#8220;<a href="#Page_45">Riveted Connections</a>.&#8221;</p>
+
+<p>It is sometimes contended that cross-girders attached at
+their ends by a riveted connection should be designed as for
+fixed ends, in which case they are usually made of the same
+flange section throughout, with a view to satisfy the supposed
+requirements. But a girder to be rightly considered
+as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction,
+and no overhead bracing, this is so far from being
+the case as to leave little occasion for taking the precaution
+named. As the cross-girders deflect, the main girders will
+commonly yield slightly, inclining bodily towards the cross-girders,
+if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in
+this manner is usually less than that which corresponds to
+fixing the cross-girder ends, and is, generally, slight. It is,
+of course, necessary that this measure of resistance at the
+connection should be borne in mind for the sake of the joint
+itself, quite apart from any question of fixing.</p>
+
+<p>Possibly, in quite exceptional cases, where very stiff
+main girders are braced in such a manner as to prevent
+canting, it may be proper to consider the cross-girder ends
+as fixed, or for those near the bearings of heavy main
+girders; but the author has not met with any example
+where cross-girders, apart from attachments, appear to have
+suffered from neglect of this consideration.</p>
+
+<p>With cross-girders placed on either side of a main girder,
+and in line, it may also, for new work, be desirable to regard
+the ends as fixed, and to detail them with this in view. It
+does not, however, appear wise to carry this assumption to
+its logical issue, and reduce the flange section to any appreciable<span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span>
+extent on this account. The fixity of the ends will, in
+any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a
+moderate effect in reducing flange stress at the middle of
+the loaded floor beam.</p>
+
+<div class="figc450"><a name="Fig13" id="Fig13"></a><a name="Fig14" id="Fig14"></a><a name="Fig15" id="Fig15"></a>
+<img src="images/illo036.png" alt="" width="450" height="315" />
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 13.</span>
+<span class="center34"><span class="smcap">Fig.</span> 14.</span> <span class="right25"><span class="smcap">Fig.</span> 15.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 13., <span class="smcap">Fig.</span> 14. and <span class="smcap">Fig.</span> 15.</p>
+</div>
+
+<p>Similar reasons affect the design of longitudinal girder
+attachments to cross-girders, which, if intended to support
+rails, cannot of necessity be schemed to come other than in
+line. Where the floor is plated as one plane surface, there
+will not usually be any trouble resulting if no special precautions
+are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving
+the joints of abnormal stress. If the plating is, however,
+designed in a manner which does not present this advantage,
+or if the floor be of timber, it is better to decide whether
+the connections shall be considered as fixed, and made so;
+or avowedly flexible, and detailed in such a manner as to
+possess a capacity for yielding slightly without injury.
+Those connections are most likely to suffer which are neither
+of the one character nor the other, offering resistance without
+the ability to maintain it. <a href="#Fig13">Figs. 13</a>, <a href="#Fig14">14</a>, and <a href="#Fig15">15</a> give representations
+of three &#8220;spring joint&#8221; methods of insuring yield
+in a greater or less degree. For small longitudinals it is,
+perhaps, sufficient to use end angles with very broad flanges
+against the cross-girder web; these to be riveted in the
+manner indicated in <a href="#Fig15">Fig. 15</a>.</p>
+
+<p>Liberal depth to floor beams is distinctly advantageous
+where it can be secured, rendering it easier to design the ends
+in a suitable manner, by giving room near mid-depth of the
+attachment to get in the necessary number of rivets; or
+where the ends are rigidly attached direct to vertical
+members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with
+a correspondingly reduced cant of the main girders and<span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span>
+flexure of the vertical member, with smaller consequent
+secondary stresses. In any case deep girders will contribute
+to stiffness of the floor itself, favourable in railway bridges
+to the maintenance of permanent-way in good order.</p>
+
+<div class="figcenter"><a name="Fig16" id="Fig16"></a><a name="Fig17" id="Fig17"></a><a name="Fig18" id="Fig18"></a>
+<img src="images/illo037.png" alt="" width="450" height="312" />
+<p class="caption"><span class="smcap">Figs.</span> 16, 17, 18.</p>
+</div>
+
+<p>A point in connection with skew-bridge floors occasionally
+overlooked is the combined effect of the skew, and main
+girder camber, in throwing the floor structure out of truth,
+if no regard has been paid to this. The result is bad cross-girder
+or other connections; or, in the case of bearers running
+over the tops of main girders, a necessity for special
+packings to bring all fair (<a href="#Fig17">Fig. 17</a>). The author has in such
+cases, where cross-girders are used, set the main girder beds
+at suitable levels, in order that the cross-bearers may all be
+horizontal (see <a href="#Fig16">Figs. 16</a> and <a href="#Fig18">18</a>). This may not always be
+permissible; but, however the difficulty may be met, it
+should be dealt with as part of the design. For small angles
+of skew only may it be neglected.</p>
+
+<p>Rivets attaching cross-girder angles to the web will occasionally<span class="pagenum"><a name="Page_25" id="Page_25">[25]</a></span>
+loosen, probably due in most cases to bad work,
+together with some circumstance of aggravation, as in the
+case of a bridge floor consisting of girders spaced 3 feet 6
+inches apart, with short timber bearers between, carrying
+rails. In many girders the top row of rivets, of ordinary
+pitch and size, had loosened, allowing the web, about <sup>1</sup>&#8260;<sub>4</sub> inch
+thick, a movement of <sup>1</sup>&#8260;<sub>8</sub> inch vertically. The rails being
+very close down upon the cross-girder tops, though not intended
+to touch, had at some time probably done so, and by
+&#8220;hammering&#8221; produced the result described.</p>
+
+<p>Plated floors are often found which are objectionable on
+account of their inability to hold water, arising sometimes
+from bad work, as often from wide spacing of rivets. With
+rivets arranged to be easily got at, and pitched not more
+than 3 inches apart, a tight floor may be expected; but it is
+still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside
+of the plate, and sufficiently long to deliver direct into
+gutters, where these are necessary. Drain-holes should not
+be less frequent than one to every 50 square feet of floor, if
+flat, and may advantageously be more so. Gutters should<span class="pagenum"><a name="Page_26" id="Page_26">[26]</a></span>
+slope well, and care be taken to insure practicable joints and
+good methods of attachment&mdash;a matter too often left to
+take care of itself, with considerable after-annoyance as a
+result.</p>
+
+<p>The use of asphalt, or asphalt concrete, to render a
+plated floor water-tight is hardly to be relied upon for railway
+bridges, though no doubt effective for those carrying
+roads. It is extremely difficult to insure that it shall stand
+the jarring and disturbance to which it may be subject, and
+under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying
+of the floor. In bulk, as in troughs, it may be useful, but
+in thin coverings on plates it cannot be depended upon.</p>
+
+<p>Floors having plated tops are sometimes finished over
+abutments or piers in a manner which is not satisfactory,
+either as regards the carrying of loads or accessibility for
+painting. If the plates are carried on to a dwarf wall with
+the intention that the free margin of the plate shall rest
+upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after
+the girder work is in place, making it difficult to insure that
+the wall really supports the plate, the result being that this
+may have to carry itself as best it can. In any case, severe
+corrosion will occur on the underside, and the plate rust
+through much before the rest of the floor; the masonry also
+will usually be disturbed.</p>
+
+<p>It appears preferable to form the end of the floor with a
+vertical skirting-plate having an angle or angles along the
+lower edge. This may come down to a dwarf wall, but preferably
+not to touch it, the skirting being designed to act
+as a carrying girder. A convenient arrangement is shown in
+<a href="#Fig19">Fig. 19</a>, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the
+skirting referred to being carried continuously along the<span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span>
+floor edge, and attached to each girder-web, the whole of the
+more important parts being open to the painter.</p>
+
+<div class="figcenter"><a name="Fig19" id="Fig19"></a>
+<img src="images/illo039.png" alt="" width="400" height="326" />
+<p class="caption"><span class="smcap">Fig.</span> 19.</p>
+</div>
+
+<p>Trough floors consisting of one or other of the forms of
+pressed or rolled section present the objection that it is almost
+impracticable to arrange an efficient connection at the ends,
+if they abut against main girders, and but little connection
+is, as a rule, attempted, and sometimes none. The result is
+that the load from these troughs is delivered in an objectionable
+manner, and the ends being open or imperfectly closed,
+water and dirt escape on to the flange, or other ledge, which
+supports them. A description of pressed floor which promises
+to overcome this objection, and provide a ready means
+of attachment to the webs of plate-girders, or of booms
+having vertical plate-webs, has within the last few years been
+introduced. This has the ends shaped in such a manner as
+to close them and provide a flat surface of sufficient area
+for connection by rivets. Each hollow is separately drained
+by holes with nozzles. Whether this type of trough will
+develop faults of its own, due to over-straining of the metal<span class="pagenum"><a name="Page_28" id="Page_28">[28]</a></span>
+in the act of pressing, remains to be seen; but as it appears
+possible to produce the desired form without any material
+thinning or thickening of the metal, the contention that no
+severe usage accompanies the process appears to be reasonable.</p>
+
+<p>That form of troughing in which the top and bottom
+portions are separately formed, and connected by a horizontal
+seam of rivets at mid-depth, is found in use upon railway
+bridges to be very liable to loosening of those rivets near the
+ends; less surprising, perhaps, because the sloping sides are
+usually thin.</p>
+
+<p>It is a distinctly difficult matter to join two or more
+lengths of any trough flooring having sloping sides, in a
+workmanlike manner; the fit of covers is apt to be imperfect,
+and some rivets, being difficult of access, are likely to be but
+indifferently tight, so that if the joint occurs where it will
+be more than lightly stressed, trouble will probably follow.
+A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most
+severe, any leakage come directly upon the girder, and remedial
+measures be more difficult to carry out.</p>
+
+<p>Timber floors of the best timber, close jointed, are more
+durable than might be supposed. The disadvantage is a
+difficulty in ascertaining the precise condition of the timber
+after many years&#8217; use. The author has seen timbers, 9 inches
+by 9 inches, forming in one length a close floor, carried by
+three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces
+with the foot; whilst in another case, with the same arrangement
+of girders and close-timbered floor, the wood, after
+being in place for thirty-two years, was, when taken out,
+found to be perfectly sound, with the exception of a very
+few bad places of no great extent. In this instance, however,
+it is known that the floor&mdash;pitch-pine&mdash;was put in by a
+contractor who prided himself upon the quality of the timber<span class="pagenum"><a name="Page_29" id="Page_29">[29]</a></span>
+that he used; the floor being also covered with tar concrete,
+which had in this instance so well performed its office as to
+keep the timber quite dry on the top.</p>
+
+<p>Jack arches between girders make an excellent floor for
+road bridges, though heavy; and for small bridges may be
+used to carry rails, if the girders are designed to be stiff under
+load. The apprehension that brickwork or concrete will
+separate from the girder-work, or become broken up under
+even moderate vibration, does not seem to be well founded, if
+the deflection is small and the brickwork or concrete good.</p>
+
+<p>The use of corrugated sheeting as a means of rendering
+the underside of a bridge drop dry cannot be too strongly
+deprecated. If it must be adopted, the arrangement should be
+such as to permit ready removal for inspection and painting.
+It is evident that by boxing up the floor structure, rust is
+favoured, and serious defects may be developed, not to be discovered
+till the sheeting is removed, or something happens.</p>
+
+<div class="figcenter"><a name="Fig20" id="Fig20"></a>
+<p class="caption"><span class="smcap">Fig.</span> 20.</p>
+<img src="images/illo042a.png" alt="" width="600" height="82" />
+</div>
+
+<p>A case may be instanced in which it was found, on taking
+down sheeting of this description, that the floor girders, previously
+hidden, were badly wasted in the webs. One of
+these girders had cracked, as shown in <a href="#Fig20">Fig. 20</a>, and others
+were in a condition only less bad.</p>
+
+<p>In any floor carrying ballast or macadam, if means are
+not adopted to keep the road material from the structure of
+the floor, or from the main girders, corrosion may be serious
+in its effects. Cinder ballast is, perhaps, the worst in this
+respect, in its action upon steel or ironwork, being distinctly
+more damaging than any other kind commonly used.</p>
+
+<p>Rail-joints upon bridge floors are to be avoided where
+practicable by the use of rails as long as can be obtained; if
+the bridge is small enough, crossing it in one length. At
+each joint there is likely to be hammering and working
+extremely detrimental to floor members and connections;
+indeed, it may happen that loose rivets will be found in the<span class="pagenum"><a name="Page_30" id="Page_30">[30]</a></span>
+neighbourhood of such joints, and nowhere else on the bridge.
+Where rail-joints cannot be
+avoided, their position should,
+if there be any choice, be judiciously
+selected, and the plate-layers
+taught to close the joints
+and jam the fish-bolts.</p>
+
+<div class="figcenter"><a name="Fig21" id="Fig21"></a>
+<img src="images/illo042b.png" alt="" width="600" height="108" />
+<p class="caption"><span class="smcap">Fig.</span> 21.</p>
+</div>
+
+<p>As rail-joints upon a bridge
+may injuriously affect the floor,
+so also will a weak floor be
+very trying to the rails. A
+remarkable instance of this has
+come under the writer&#8217;s notice,
+where a bridge (<a href="#Fig21">Fig. 21</a>) of
+three 33-feet spans, having
+outer and centre main girders,
+with cross-girders spaced 3 feet
+apart, resting upon the girder
+flanges, but not attached, and
+carrying two roads, had the permanent-way
+in a very bad state.
+The rails proper, with supplementary
+angle-plates, rested
+direct upon the cross-girders,
+which were decidedly light,
+and the whole floor had much
+&#8220;life&#8221; in it, the ill-effect of
+which was shown in thirteen
+breaks in the angle-plates, in
+each case near their ends,
+generally at holes.</p>
+
+<p>It appears probable that
+severe stresses may be thrown
+upon the parts of a floor,<span class="pagenum"><a name="Page_31" id="Page_31">[31]</a></span>
+whether placed at the level of the bottom booms or of
+the top, by changes of length in the booms due to stress.
+The author has, unfortunately, no direct evidence to offer
+in reference to this, tending either for or against the contention.
+If an unplated floor of cross and longitudinal
+girders of usual arrangement be at the bottom boom of
+a large bridge, as the boom lengthens with the imposition
+of load upon the bridge, all the cross-girders from the
+centre towards the abutments will be curved horizontally,
+the middle portion being restrained by the longitudinals
+from moving bodily with the ends. Each cross-girder
+except that at the centre, if there be one, will thus present
+a figure in plan, concave towards the abutment to which it
+is nearest. This will be accompanied by stressing of the
+connections, and a transfer to the longitudinals of as much
+of the tensile stress properly belonging to the booms as the
+stiffness of the cross-girders may communicate.</p>
+
+<p>This in itself will hardly be considerable, and will be the
+less on account of a slight yielding which may be expected
+at the end connections of each longitudinal; but the effect
+upon the cross-girders by horizontal bending will be much
+marked. If the case be supposed of a 200-feet span in steel
+at ordinary loads and stresses, carrying one line of way, with
+cross-girders 20 feet apart, and having no floor-plates, it may
+be ascertained, neglecting for the moment any slight yielding
+of the longitudinal girder connections, that upon the bridge
+taking its full live load there will be the following approximate
+results: Movement at each end of the end cross-girders
+of <sup>3</sup>&#8260;<sub>10</sub> inch, equivalent to a force of 7<sup>1</sup>&#8260;<sub>2</sub> tons, tending to bend
+them horizontally, and a mean stress on the outer edges of the
+girders, 12 inches wide, of 8 tons per square inch due to
+flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge,<span class="pagenum"><a name="Page_32" id="Page_32">[32]</a></span>
+of <sup>3</sup>&#8260;<sub>4</sub> ton per square inch. Normal elongation of the longitudinal
+girder bottom flanges, and compression of the top, modifies
+the figures unfavourably as to the cross-girder top flange.
+Yielding of the connections named before has been neglected
+in arriving at these stresses. If they are sufficiently accommodating
+to give freely, to a mean extent, as between the
+top and bottom of each joint, of <sup>1</sup>&#8260;<sub>29</sub> inch, these results will
+disappear. It is evident, however, that we cannot rely upon
+good work yielding without the existence of considerable forces
+to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.</p>
+
+<p>The most favourable case has been taken; if now it is
+assumed that the floor has continuous plating, the results
+would seem to be much more astonishing. It will appear on
+this supposition that the boom stresses, instead of being
+taken wholly by the booms, are about equally divided between
+these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which
+for the end cross-girders will approach 40 tons at each
+connection&mdash;considerably more than the vertical reaction
+under normal loads.</p>
+
+<p>Palpably, these conclusions must be greatly modified by
+the yield of longitudinal girder ends, and slip of the floor
+rivets in transverse seams. If these rivets be 3<sup>1</sup>&#8260;<sub>2</sub> inch pitch
+and <sup>3</sup>&#8260;<sub>4</sub> inch in diameter, the stress at each, as estimated, would
+be sufficient to induce shear of about 6 tons per square inch&mdash;more
+than enough to cause &#8220;slip.&#8221; After making this allowance,
+it is still evident there must be very serious forces at
+work about the ends of cross-girders under the conditions supposed,
+probably not less than one half the amounts named, as
+with this reduction the floor rivets should not yield, given
+reasonably good work. It is to be observed that the effect of
+live load only has been introduced, on the presumption that the
+longitudinals and floor-plating have not been riveted up till<span class="pagenum"><a name="Page_33" id="Page_33">[33]</a></span>
+the main girders have been allowed to carry the major part
+of the dead load; but even this cannot always be conceded.
+The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these
+possible effects, either with the object of rendering the communication
+of these forces harmless, or making the floor so
+that it shall take little or no stress from the main booms, by
+arranging joints across the floor specially designed to yield,
+the ends of longitudinals being schemed with the same object.
+Where there is no plating, the case is, perhaps, sufficiently
+provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these
+girders upon the top of the cross-girders, when stretching of
+the bottom flanges of the rail-bearers under load may be
+expected, within a little, to keep pace with the lengthening
+of the main booms.</p>
+
+<p>It would appear that light pressed troughs running across
+the longitudinals would, by yielding in every section, also
+furnish relief, as compared with the rigidity of flat plates.</p>
+
+<p>By placing the floor at a level corresponding to the
+neutral axis of the main girders, the communication of stress
+to the floor may be avoided; but it seldom happens that
+there is so free a choice as to floor height relative to the
+girders. This solution is, therefore, of limited application.</p>
+
+<p>It is obvious that somewhat similar effects must obtain to
+those considered in detail, when the floor structure lies at the
+level of top booms, but with forces of compression from the
+booms to deal with, instead of tension.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_34" id="Page_34">[34]</a></span></p>
+
+<h2>CHAPTER IV.<br />
+<span class="chaptitle">BRACING.</span></h2>
+
+<p>Bracing, whether to strengthen a structure against wind, to
+insure the relative positions of its parts, or for any other
+purpose, cannot be arranged with too great care and regard
+to its possible effects. Forces may be induced which the
+connections will not stand, with loose rivets as a consequence,
+and inefficiency of the bracing itself; or, the connections
+holding good, stresses in the main structure may, perhaps,
+be injuriously altered.</p>
+
+<p>To take a not uncommon case, let us suppose a bridge
+consisting of four main girders placed immediately under
+rails of ordinary gauge, and braced in vertical planes only,
+right across from one outer girder to the other. If the
+roads were loaded always at the same time, nothing objectionable
+would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and
+deflects, the bracing under the six-foot will endeavour to
+communicate some part of this load to the other pair of
+girders. If the bracing is so designed that some correctly
+calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections,
+there will be no harmful consequences; but if not, the
+bracings will most probably work at the ends; this, indeed,
+is what frequently happens. There is one other effect which
+will ensue, if the bracing is wholly efficient; a certain twisting
+movement of the bridge will occur, which increases the
+live load upon the outer girder on the loaded side of the<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span>
+bridge to the extent of 10 per cent., with a corresponding
+lifting force at the outer girder on the unloaded side. These
+amounts are not serious, but wholly dispose of any advantage
+it is conceived will be gained by causing the otherwise idle
+girders to act through the medium of the bracing. In road
+bridges of similar arrangement, over which heavy loads may
+pass on any part of the surface, it is clear that the use of
+bracing between girders should not be taken as justifying
+the assumption that the load is distributed over many girders,
+and correspondingly light sections adopted, unless the effect
+of twisting on the whole bridge is also considered, and justifies
+this view; for, as already stated in the case of the railway
+bridge, the net result may be to increase the girder stresses
+instead of reducing them. Generally, it may be deduced
+that the better plan for railway bridges is to brace the girders
+in pairs, leaving, in the case supposed, no bracing between
+the two middle girders, though there will be no objection to
+connecting these by simple transverse members of no great
+stiffness, to assist in checking lateral vibration. For road
+bridges of more than five longitudinal girders, equally spaced,
+it may be advantageous to brace right across, the twisting
+effect with this, or a greater, number of girders not, as a rule,
+leading to any increase of load on any girder. <a href="#Fig22">Figs. 22</a> to
+<a href="#Fig25">25</a> give the distribution of live load, placed as shown, for 3,
+4, 5, and 6 girders.</p>
+
+<p>It is to be observed that these statements do not apply to
+cases where there may be also a complete system of horizontal
+bracing, the effect of which, in conjunction with cross
+diagonals, may be greatly different, with considerable forces
+set up in the bracing, and a modification of girder stresses.</p>
+
+<p>These effects may be so considerable as to call for special
+attention in design where such an arrangement is adopted.</p>
+
+<div class="figc600"><a name="Fig22" id="Fig22"></a><a name="Fig23" id="Fig23"></a><a name="Fig24" id="Fig24"></a><a name="Fig25" id="Fig25"></a>
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 22.</span> <span class="right60"><span class="smcap">Fig.</span> 24.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 22. and <span class="smcap">Fig.</span> 24.</p>
+
+<img src="images/illo048.png" alt="" width="600" height="235" />
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 23.</span> <span class="right60"><span class="smcap">Fig.</span> 25.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 23. and <span class="smcap">Fig.</span> 25.</p>
+</div>
+
+<p>Somewhat similar straining to that first indicated may
+occur in bracings placed between the girders of a bridge<span class="pagenum"><a name="Page_36" id="Page_36">[36]</a></span>
+much on the skew. If this is, on plan, at right angles to
+the girders, as is commonly and properly the case, the ends
+will evidently be attached to the girders at points on their
+length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts,
+and the bracing will, if at one end attached near a rigid
+bearing, transfer some part of the load from one girder to<span class="pagenum"><a name="Page_37" id="Page_37">[37]</a></span>
+the other, notwithstanding that both girders may be of the
+same span and equal extraneous loading. It would not be
+difficult to ascertain the amount of load so transferred from
+a consideration of the relative movements if free, and the
+loads on the two girders necessary to render these movements
+equal, if the deflections were simply vertical; but as there
+will be some twisting and yielding of the girders on their
+seats, the calculation becomes involved. If the bracing is
+placed at about the middle of the girders, the effects noted
+will be greatly reduced; first, because the difference of
+movements near the centre will be less; second, any given
+difference will correspond to a smaller transference of load;
+and, third, because each girder will there be more free to
+twist than at the ends. It therefore appears that bracings
+between the girders of a skew bridge should not be placed
+near the bearings, though they may be put, with much less
+risk of injury, near the middle.</p>
+
+<p>Cross-girders on a skew bridge are subject to forces
+somewhat similar to those which may affect bracing, rendering
+it desirable to design their attachments in a manner
+which shall not aggravate the matter, but rather reduce the
+effects of unequal vertical displacement of their ends where
+secured to the main girders.</p>
+
+<p>Crossed flat bars as bracing members are objectionable
+on account of their tendency to rattle, after working loose;
+but as this effect only ensues in bracing which has first
+become loose (it being assumed that the bars in any case are
+connected where they cross), this objection is not itself vital,
+though greater rigidity is easily obtained by making all such
+members of a stiff section.</p>
+
+<p>Defective bracing between girders, from neglect of the
+very considerable forces it may be called upon to communicate,
+is very common; the writer has seen many such cases,
+of which one is here illustrated in <a href="#Fig26">Fig. 26</a>.</p>
+
+<p><span class="pagenum"><a name="Page_38" id="Page_38">[38]</a></span></p>
+
+<div class="figcenter"><a name="Fig26" id="Fig26"></a>
+<img src="images/illo050.png" alt="" width="600" height="298" />
+<p class="caption"><span class="smcap">Fig.</span> 26.</p>
+</div>
+
+<p>This bridge, of the section shown, and 85 feet span, had
+very light web structure. The bracings, of which there
+were two sets, were wholly inefficient, the end rivets being
+loose in enlarged holes. Upon the passage of a train there
+was a positive lurching of the girder tops from side to side.<span class="pagenum"><a name="Page_39" id="Page_39">[39]</a></span>
+The integrity of the bridge was really dependent upon such
+stiffness as there was in the girders, and unplated floor.</p>
+
+<p>A common but indifferent method of keeping the top
+members of main girders in line is by the use of overhead
+girders alone, frequently curved to give the requisite clearance
+over the road. This cannot be considered as wholly
+inefficient, as sometimes maintained, since it is evident that
+the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must
+take a greater force to distort it than would be necessary to
+cause deformation of a corresponding degree, in an open
+frame formed by the omission of the overhead girder; but it
+is not a method to be recommended, its precise utility is
+difficult to estimate, and, if the cross-girder attachments are
+of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however,
+not applicable to this arrangement alone. All overhead
+bracing favours this by restraining the tendency of the top
+booms to cant inwards when the floor beams are loaded; and
+though this restraint may be quite harmless, it is desirable
+that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in
+its character. &#8220;Sway&#8221; bracing, sometimes introduced at
+right angles to the bridge between opposite verticals, tends
+to emphasise these effects by rendering the cross-section of
+the bridge still stiffer, besides making it a matter of difficulty
+to ascertain how much of the wind forces on the top boom
+is carried to the abutment by the top system of bracing, and
+how much by the floor. The author does not, however, mean
+to suggest that it cannot be used with propriety, but rather
+that extreme care is desirable in considering its ultimate
+effect on the rest of the structure.</p>
+
+<p>For girders of moderate depth there may be on these
+grounds a distinct advantage in abandoning overhead bracing,<span class="pagenum"><a name="Page_40" id="Page_40">[40]</a></span>
+and securing rigidity of the top boom, and adequate
+resistance to wind forces, by making the connection between
+the cross-girders and the web members sufficiently good to
+insure, as a whole, a stiff <span class="lettsymb">U</span>-shaped frame; but this, with
+the ordinary type of rocker arrangement under the main
+girder bearings, will not be entirely free from objection, as
+canting of the girders due to floor loading will throw extreme
+pressure on the inner end of each rocker. There appears to
+be no reason why the cylindrical knuckle should not in this
+case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.</p>
+
+<div class="figcenter"><a name="Fig27" id="Fig27"></a>
+<img src="images/illo053.png" alt="" width="300" height="357" />
+<p class="caption"><span class="smcap">Fig.</span> 27.</p>
+</div>
+
+<p>The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom
+flanges, renders very narrow top booms permissible. This is
+a decided advantage where lightness of appearance is aimed
+at; but it is not unusual to see an attempt made in this
+direction by introducing gusset plates of very ample proportions
+between vertical members of the girders, and the projecting
+ends of flimsy transoms, carried beyond the width of
+the bridge proper, these being of a section wholly out of
+proportion to the brackets they are supposed to secure.
+Whatever may be the amount of strength necessary at the
+point A, in <a href="#Fig27">Fig. 27</a>, there should not be less throughout the
+transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the
+vertical stiffeners is not, as a rule, great. Information to
+enable this question to be dealt with as a matter of calculation
+is somewhat scanty; but it would appear to be sufficient
+to insure safety that, for an assumed small amount of curvature
+in the compression member, the forces outwards corresponding
+to this curvature, due to thrust, should be resisted
+by verticals and transoms of strength and stiffness sufficient
+to restrain it from any further flexure. It will, of course,
+be necessary also to take care that the compression member<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span>
+is good as a strut between the points of restraint. A
+simple and sufficiently precise method of dealing with this
+question is much needed. In cases where the floor weight
+rests on the flange projection, it is also necessary to give
+the transom additional strength to an extent enabling it
+to resist the twisting effort between any two of these
+transverse members; further, resistance to wind on the
+girder has to be provided in both transoms and verticals.</p>
+
+<p>It may be hardly
+necessary to insist
+that bracing intended
+to stiffen a structure
+against wind, local
+crippling, or vibration,
+should be made
+complete, not stopping
+short at some
+point, because it cannot
+conveniently be
+carried further, as
+is sometimes done,
+unless the strength
+of those parts of
+the structure through
+which the forces from
+the bracing must be communicated to the abutments is
+sufficiently great, considered with reference to other stresses
+in those parts which have also to be endured.</p>
+
+<p>Bracing stopped short in this way, making only the
+central part of a bridge rigid, may have the effect of increasing
+the forces to which the unstiffened end members would
+otherwise be liable. Such a structure would evidently be
+much stiffer against wind-gusts than if no bracing existed&mdash;the
+resistance to a blow would be increased; but the power to<span class="pagenum"><a name="Page_42" id="Page_42">[42]</a></span>
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater
+maximum forces than if bracing were wholly omitted. The
+net effect may still be better than with no bracing, the point
+raised being simply that of an increase of stress in particular
+end members.</p>
+
+<p>In the bracing of tall piers, the rising members of which
+will be subject to any considerable stress, if the diagonal
+members are not finally secured when the piers are under
+their full load, or an initial stress of proper amount induced
+in those members, the effect of loading will be to render
+them slack; so that an appreciable amount of movement at
+the top may occur before it can be limited by the efficient
+action of the bracings. This effect under blasts of wind or
+continual passage of trains may, indeed, be dangerous.
+Similar considerations apply to the top wind bracing of deep
+girder bridges, influencing also the bottom bracing in a contrary
+manner, which calls for attention in fixing the unit
+stresses for such members.</p>
+
+<p>The bracing of sea-piers is very liable to slacken if made
+with pin-and-eye ends, as is often done for round rods. The
+detail presents advantages in erection, but is not altogether
+satisfactory in practice. Such connections are continually
+working. In the finest weather, with the sea quite smooth
+but for an almost imperceptible wave movement, the lower
+parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there
+room for surprise when it is considered that these oscillations,
+occurring at about ten to each minute, never wholly cease,
+and amount in the course of one year to over five million in
+number.</p>
+
+<p>Bracing attached in such a manner that there can be no
+initial slack, or slack due to wear under endless repetitions
+of small amounts of stress, will have a much better chance to<span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span>
+keep tight. The advantage presented by round rods in
+offering little surface to the water, is more than negatived
+by inefficiency of the usual attachments for such rods.</p>
+
+<p>The author has observed that bracing of members possessing
+some stiffness, and with good end attachments to ample
+surfaces, appears to stand best in ordinary sea-pier work.
+For such structures the bracing should consist of a few
+good members, with a solid form of attachment, rather than
+of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very
+possibly also, in the case of sea-pier work, in unskilled hands.
+If round rods must be used, they will stand much better if
+made of large diameter.</p>
+
+<p>Before leaving the subject of bracing, it may not be out
+of place to refer to wind pressure, as this may so much affect
+the proportioning of the members.</p>
+
+<p>Some years since the author had occasion to examine a
+number of structures with respect to their stability. Of foot-bridges
+from 60 feet to 120 feet long, three or four, when
+calculated on the basis recommended by the Board of Trade
+as to pressures upon open-work structures, worked out at an
+overturning pressure of from 18 lb. to 22 lb. per square foot.
+These bridges had been many years in existence; it is,
+therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them
+as to the whole surface.</p>
+
+<div class="figcenter"><a name="Fig28" id="Fig28"></a>
+<img src="images/illo056.png" alt="" width="400" height="333" />
+<p class="caption"><span class="smcap">Fig.</span> 28.</p>
+</div>
+
+<p>Particulars were taken in 1895 of a notice-board, presenting
+about 12 square feet of surface, which was blown down
+in the great storm of March 24 of that year, at Bilston, in
+Staffordshire. It was situated at the foot of a slight slope,
+over which the wind came, striking the obstruction at right
+angles. The board was mounted on two oak posts of fair
+quality and condition, which broke near the ground at bolt
+holes (see <a href="#Fig28">Fig. 28</a>). The force required to do this, at 9000 lb.<span class="pagenum"><a name="Page_44" id="Page_44">[44]</a></span>
+modulus of rupture&mdash;a moderate value&mdash;corresponds to 50 lb.
+per square foot on the surface exposed above the break.</p>
+
+<p>In the same neighbourhood, at the same time, considerable
+damage was wrought in overturning chimney stacks, to
+buildings and roofs; the general impression in the locality
+being that the storm was of exceptional, even unprecedented,
+violence. Bilston, it should be noted, lies high.</p>
+
+<p>At Bidston Hill, near Birkenhead, on the same occasion,
+a pressure of 27 lb. was registered. In another part of the
+country it is said to have been 37 lb. Wind is so capricious
+in its effects over small areas as to render it probable that the
+maximum pressures have never been recorded; but this is
+a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by
+themselves insufficient to throw much light on the question,
+may be of use in connection with other known examples.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span></p>
+
+<h2>CHAPTER V.<br />
+<span class="chaptitle">RIVETED CONNECTIONS.</span></h2>
+
+<p>Considerable latitude is observable in the practice of
+engineers in the use of rivets. Numberless experiments to
+determine the resistance of riveted connections have from
+time to time been made, but these are not to be considered
+by themselves as final, when the results of experience in
+actual construction, are available for further enlightenment.</p>
+
+<p>The class of workmanship so largely influences the degree
+in which rivets will maintain their integrity that it is only
+by the observation of a large number of cases, including all
+degrees of workmanship, that any reliable conclusions may
+be drawn. In this respect laboratory experiments have an
+apparent advantage, as the conditions may be kept sensibly
+the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must
+in the end determine the utility of any inquiry for practical
+application.</p>
+
+<p>The author has studied the particulars of a number of
+cases to ascertain under what conditions as to stress, having
+due regard to the effects of vibration, rivets will remain tight,
+or become loose. Every loose rivet that may be found cannot,
+of course, be taken as being due to excessive stress; the more
+frequent cause is indifferent work, evidenced by the fact that
+neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon
+the remainder. When rivets loosen as the direct result of
+over-stress, it is usually by compression of the shank and<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span>
+enlargement of the hole, or by stretching of the rivet and
+reduction of its diameter. Instances of failure by partial or
+complete shear are extremely rare; indeed, the author has
+never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work,
+it is not uncommon to find it cut or bent as an after consequence.</p>
+
+<p>In estimating stresses at which rivets have remained
+tight, or loosened, as the case may be, examples have generally
+been chosen in which there could be no reasonable
+doubt as to the amount of those stresses by the ordinary
+methods of computation. This is clearly most important,
+as, if any appreciable uncertainty remained as to the degree
+of stress, the results deduced would be of little value. For
+this reason those instances in which the loads upon girders,
+or parts of girders, may find their way to the supports by
+more than one route, are to be regarded with caution, as are
+those in which full loading possibly never obtains, but which
+may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been
+used in making the computations; in some cases from
+direct measurement from particular rivets, in others with a
+suitable allowance for excess diameter of hole, according to
+the class of work under consideration.</p>
+
+<p>Dealing first with main girders, it may be said that rivets
+attaching the webs of plate girders to the flange angles rarely
+loosen, though subject to considerable stress. In illustration
+of this may be named a bridge for two lines of way, 85 feet
+effective span, having two main girders with plate webs, and
+cross-girders resting on the top flanges, previously referred
+to (see <a href="#Fig26">Fig. 26</a>).</p>
+
+<p>The girders, which were 6 feet 9 inches deep, had a bearing
+upon the abutments of 4 feet; the rivets were <sup>7</sup>&#8260;<sub>8</sub> inch in
+diameter and 4 inches pitch. There is in a case of this kind<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span>
+some little uncertainty as to what is the stress on the flange
+angle rivets at, or very near to, the bearings; but, taking
+the vertical rows of rivets at the web joints near the ends as
+presenting less uncertainty, the stress per rivet works out at
+4&middot;8 tons, being 4 tons per square inch on each shear surface,
+and 11 tons per square inch bearing pressure upon the shank
+in the web plate, which was barely <sup>1</sup>&#8260;<sub>2</sub> inch thick. This bridge
+was frequently loaded upon both roads, but with one road
+only carrying live load, the stresses in the more heavily
+loaded girder would be fully 90 per cent. of those obtaining
+as a maximum. There was on this bridge, which had been
+in use 31 years, considerable movement and vibration.</p>
+
+<p>It is by no means uncommon to find cases of rivets in
+main girders taking 11 tons per square inch bearing pressure&mdash;occasionally
+more&mdash;and remaining tight. As furnishing
+an instructive, though slightly ambiguous, instance of rivets
+in single shear, may be cited a bridge not greatly less than
+that just referred to, of about 65 feet span, carrying two
+lines of way, there being two outer and one centre main
+girder of multiple lattice type, with cross-girders in one
+length 4 feet apart, riveted to the bottom booms of the main
+girders; these rivets, by the way, were in tension. The
+floor was plated, the road consisting of stout timber longitudinals,
+chairs, and rails (<a href="#Fig29">Fig. 29</a>).</p>
+
+<div class="figcenter"><a name="Fig29" id="Fig29"></a>
+<img src="images/illo060.png" alt="" width="600" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 29.</p>
+</div>
+
+<p>It should be noted that there is in this case some difficulty
+in ascertaining the precise behaviour of the cross-girders,
+affecting the proportion of load carried by the outer
+and the inner main girders. Strict continuity of all the
+cross-girders could only obtain if the deflection of the main
+girders were such as to keep the three points of suspension of
+each cross-girder in the same straight line. A close inquiry
+showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would,
+under load, by relative depression of the middle point of<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span>
+support, be reduced to the condition of two simple beams,
+those at the extreme ends of the span would behave as
+continuous girders.</p>
+
+<p>With both roads carrying
+engine loads equal to those
+coming upon the bridge, the
+author estimates that for the
+centre main girder the shear
+on the rivets of the end diagonals,
+secured by one rivet
+only, was 14&middot;9 tons per square
+inch, and the bearing pressure
+16&middot;3 tons; the flange stress
+being 7&middot;1 tons per square inch
+net. The outer main girders
+are most heavily stressed when
+but one road, next to the
+outer girder considered, carries
+live load. For this condition
+the stresses work out at
+9 tons per square inch shear
+on the rivets of the end diagonals,
+and 9 tons bearing
+pressure, the flange stress being
+5&middot;7 tons per square inch
+on the net section.</p>
+
+<p>Without intending to
+throw any doubt upon the
+substantial truth of these
+results, it must be admitted
+that instances of greater simplicity
+of stress determination
+are much to be preferred. For purposes of comparison, but
+not as having any other value, the results have also been<span class="pagenum"><a name="Page_49" id="Page_49">[49]</a></span>
+worked out on the supposition of all cross-girders acting
+each as two simple beams, and also for strict continuity, and
+are here tabulated, together with the conclusions given above.</p>
+
+<p>The cross-girders were moderately stressed, and the tension
+on the rivets attaching them to the main girders
+probably did not exceed 3 tons per square inch.</p>
+
+<p>It should be pointed out that the traffic over the bridge
+was small. The centre main girder but seldom bore its full
+load, though at all times liable to receive it. Much importance
+cannot, therefore, be attached to the results for this
+girder, other than as showing how a structure may stand for
+many years, though liable at any time to the development
+of stresses which would commonly be regarded as destructive,
+or nearly so.</p>
+
+<p class="center"><span class="smcap">Examples of Rivet Stresses, etc., in Lattice Girders.</span></p>
+
+<table class="nowrap" summary="Table page 49">
+
+<tr class="bt bb">
+<th rowspan="2" class="br">&mdash;</th>
+<th class="br">Cross-<br />Girders<br />as Simple<br />Beams.</th>
+<th class="br">Cross-<br />Girders<br />as Con-<br />tinuous<br />Beams.</th>
+<th>Correct<br />Results.</th>
+</tr>
+
+<tr class="bb">
+<th colspan="3">Stress in Tons per Square Inch.</th>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Centre girder, 63 ft. span (both roads loaded):</td>
+<td class="br">&nbsp;</td>
+<td class="br">&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">Rivets in diagonals&mdash;Shear</td>
+<td class="right padl1 padr2 br">13&middot;7</td>
+<td class="right padl1 padr2 br">17&middot;2</td>
+<td class="right padl1 padr2">14&middot;9</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals&mdash;</span><span class="padl0">Bearing pressure</span></td>
+<td class="right padl1 padr2 br">15&middot;0</td>
+<td class="right padl1 padr2 br">18&middot;8</td>
+<td class="right padl1 padr2">16&middot;3</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals&mdash;</span><span class="padl0">Flange stress</span></td>
+<td class="right padl1 padr2 br">6&middot;8</td>
+<td class="right padl1 padr2 br">8&middot;5</td>
+<td class="right padl1 padr2">7&middot;1</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br blankabove">Outer girder, 66 ft. span (near road loaded):</td>
+<td class="br blankabove">&nbsp;</td>
+<td class="br blankabove">&nbsp;</td>
+<td class=" blankabove">&nbsp;</td>
+</tr>
+
+
+<tr>
+<td class="padl3 padr1 br">Rivets in diagonals&mdash;Shear</td>
+<td class="right padl1 padr2 br">9&middot;6</td>
+<td class="right padl1 padr2 br">8&middot;2</td>
+<td class="right padl1 padr2">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals&mdash;</span><span class="padl0">Bearing pressure</span></td>
+<td class="right padl1 padr2 br">9&middot;6</td>
+<td class="right padl1 padr2 br">8&middot;2</td>
+<td class="right padl1 padr2">9&middot;0</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals&mdash;</span><span class="padl0">Flange stress</span></td>
+<td class="right padl1 padr2 br">5&middot;9</td>
+<td class="right padl1 padr2 br">5&middot;1</td>
+<td class="right padl1 padr2">5&middot;7</td>
+</tr>
+
+</table>
+
+<p>The material and workmanship of the bridge were good.
+The rivets of the centre girder end diagonals, 1 inch in
+diameter, were originally <sup>7</sup>&#8260;<sub>8</sub> inch, but on becoming loose were<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span>
+cut out, the holes reamered, and replaced by the larger size,
+which remained tight, and to which the stress figures apply.
+The rivets in the diagonals near the centre, <sup>7</sup>&#8260;<sub>8</sub> inch in diameter,
+which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The
+riveting in the outer girder diagonals, subject to smaller
+stresses, much more frequently developed, also gave trouble,
+particularly those liable to counter stresses.</p>
+
+<p>Apart from looseness of rivets, the general appearance
+and behaviour of the bridge, which had been in existence
+about twenty years, was not suggestive of any weakness.</p>
+
+<p>Of smaller girders, an example showing the necessity for
+care in discriminating, if it be possible, between looseness
+of rivets resulting from over-stress and that due to other
+influences may first be quoted. Two trough girders, of
+11 feet effective span, each of the section shown in <a href="#Fig30">Fig. 30</a>,
+11<sup>1</sup>&#8260;<sub>2</sub> inches deep at the ends, 14 inches at the middle, with
+<sup>1</sup>&#8260;<sub>4</sub>-inch webs, and rivets <sup>3</sup>&#8260;<sub>4</sub> inch in diameter, of 4<sup>1</sup>&#8260;<sub>2</sub>-inch pitch,
+showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (<a href="#Fig31">Fig. 31</a>). From the nature
+of the arrangement the lower web rivets, which were loose,
+would receive the first shock of the load coming upon the
+span, but there were evidences indicative of original bad
+work. The angle bars gaped, suggesting that these had
+first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets
+failing to pull the work close, and then readily working loose.
+Here there is considerable uncertainty as to how much of
+the loosening is to be attributed to bad work, and how much
+to stress. It may, however, be remarked that whatever
+bearing stress was the ultimate result of the load hammering
+on the lower angle flanges, loosening rivets never perhaps
+really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable<span class="pagenum"><a name="Page_51" id="Page_51">[51]</a></span>
+impactive force, was not sufficient to loosen these. The
+girders were taken out after being in place sixteen years.</p>
+
+<div class="figc600"><a name="Fig30" id="Fig30"></a><a name="Fig31" id="Fig31"></a><a name="Fig32" id="Fig32"></a>
+<p class="caption_b"><span class="left53"><span class="smcap">Fig.</span> 30.</span> <span class="right46"><span class="smcap">Fig.</span> 32.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 30. and <span class="smcap">Fig.</span> 32.</p>
+<img src="images/illo063.png" alt="" width="600" height="320" />
+<p class="caption"><span class="smcap">Fig.</span> 31.</p>
+</div>
+
+<p>An instance of undoubted excessive bearing pressure
+was found in the cross-girders of a bridge, mentioned on
+<a href="#Page_15">p. 15</a>, of which so many web plates were cracked. This
+bridge, carrying two lines of way, had outer main girders,
+and long cross-girders with <sup>1</sup>&#8260;<sub>4</sub>-inch webs and <sup>3</sup>&#8260;<sub>4</sub>-inch rivets,<span class="pagenum"><a name="Page_52" id="Page_52">[52]</a></span>
+4 inches pitch. The rivet stresses work out at 4&middot;3 tons per
+square inch on each shear surface, and 24 tons per square
+inch bearing pressure. For
+one road only being loaded, the
+latter figure falls to 18&middot;5 tons.
+The traffic over this bridge,
+twenty years old, was considerable,
+rapid, and heavy. It is
+hardly necessary to add that
+a large number of the rivets
+were loose, one of which is
+shown in <a href="#Fig32">Fig. 32</a>.</p>
+
+<div class="figcenter"><a name="Fig33" id="Fig33"></a>
+<img src="images/illo064.png" alt="" width="600" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 33.</p>
+</div>
+
+<p>To take another case relating
+to a floor system of extremely
+bad design (<a href="#Fig33">Fig. 33</a>).
+The main girders were 11 feet
+apart, 35 feet span, the floor
+having two cross-girders only,
+spaced at 11 feet 3 inches, and
+9 inches deep, supporting hog-backed
+trough longitudinals.
+The cross-girders were at their
+ends but 6<sup>3</sup>&#8260;<sub>4</sub> inches deep, the
+distance from the bearing of
+cross-girders to centre of longitudinals
+carrying a rail being
+2 feet 10 inches, in which
+length were eight rivets in the
+web and angles at the top, and
+six at the bottom, all <sup>3</sup>&#8260;<sub>4</sub> inch in
+diameter.</p>
+
+<p>The shear stress on the upper rivets works out at 7&middot;3
+tons per square inch on each shear surface, the bearing pressure
+20&middot;6 tons per square inch. On the lower rivets the<span class="pagenum"><a name="Page_53" id="Page_53">[53]</a></span>
+shear stress becomes 9&middot;7 tons, and the bearing pressure
+27&middot;4 tons, per square inch. Care was exercised in computing
+these stresses, that part of the bending moment
+carried by the web being allowed for, but it must be admitted
+that the result is, probably, approximate only. The <a href="#Fig33">sketch</a>
+here given shows the cross-girder end and section. The
+rivets, though in double shear, were, as might be expected,
+loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled
+after twelve years&#8217; use.</p>
+
+<p>In illustration of the behaviour of rivets in the ends of
+long cross-girders, both shallow and weak, and many years
+in use under heavy traffic, may be cited connections having
+end angle bars to the cross-girders, with six rivets through
+the web of main girders. The bearing pressure worked out
+at 7&middot;8 tons per square inch. Many rivets were loose, but it
+should be remarked that the workmanship was not of the
+best class, and the cross girders flexible: a characteristic
+very trying to end rivets, and inducing a stretch in some,
+already referred to as a possible cause of loosening. This
+will be apparent if the probable end slope of weak girders
+be considered. The author concludes that this inclination
+should not, for ordinary cases, exceed 1 in 250; but the
+ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly
+regarded as bad practice to submit rivets to tension, yet this
+is frequently, though unintentionally, permitted in end attachments,
+without any attempt to limit the amount of
+tension. With suitable restrictions, there appears no serious
+objection to rivet tension for many situations.</p>
+
+<p>Another instance of cross-girder end connections of a
+different type is illustrated in <a href="#Fig34">Fig. 34</a>.</p>
+
+<div class="figcenter"><a name="Fig34" id="Fig34"></a>
+<img src="images/illo066a.png" alt="" width="300" height="328" />
+<p class="caption"><span class="smcap">Fig.</span> 34.</p>
+</div>
+
+<p>The main girders of the bridge were 12 feet apart, each
+cross-girder end carrying its share of the half of one road.<span class="pagenum"><a name="Page_54" id="Page_54">[54]</a></span>
+The mean bearing pressure upon the rivet shanks works out
+at 5&middot;8 tons per square inch for the six rivets of the original
+joint, but in the particular joint shown some of the rivets
+had loosened, making the bearing pressure upon the remainder
+about 8&middot;7 tons per square inch. It is apparent
+there must have been considerable stress on the top and
+bottom rivets which loosened. These two rivets would also,
+because of difficult access, be in all likelihood insufficiently
+hammered up. The joints worked rather badly; the loose
+rivets had &#8220;cut&#8221; to a considerable extent, a process materially
+assisted by the gritty nature of the ballast (limestone),
+particles of which, getting into the joint, contributed to the
+sawing action; this had clearly been taking effect for some
+considerable time. (See <a href="#Fig35">Fig. 35</a>.)</p>
+
+<div class="figcenter"><a name="Fig35" id="Fig35"></a>
+<img src="images/illo066b.png" alt="" width="350" height="219" />
+<p class="caption"><span class="smcap">Fig.</span> 35.</p>
+</div>
+
+<p>The two cases of cross-girder ends given are both rather
+exceptional in character, and in each case the defects appear
+to be due to general bad design and workmanship rather
+than to any serious excess of bearing pressure. This may
+be illustrated by taking the common case of cross-girders,
+2 feet deep, carrying two roads, and having end angle irons
+riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span>
+is, for old work, simply typical, and does not relate to any
+specific instance, the bearing pressure on the rivets will work
+out at from 6 to 8 tons per square inch, and will seldom be
+accompanied by looseness of rivets, and then only as a result
+of faulty work.</p>
+
+<p>Some sketches of rivets taken from old bridges have
+already been given in connection with the cases to which
+they belong; a few others are here shown (<a href="#Fig36">Figs. 36</a> to <a href="#Fig40">40</a>)
+to further illustrate what may be the actual condition of
+rivets after some years&#8217; use, and how different from the ideal
+rivet upon which calculations are based. These are, however,
+bad instances.</p>
+
+<div class="figc350"><a name="Fig36" id="Fig36"></a><a name="Fig37" id="Fig37"></a>
+<img src="images/illo067a.png" alt="" width="350" height="88" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 36.</span> <span class="right49"><span class="smcap">Fig.</span> 37.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 36. and <span class="smcap">Fig.</span> 37.</p>
+</div>
+
+<div class="figc350"><a name="Fig38" id="Fig38"></a><a name="Fig39" id="Fig39"></a>
+<img src="images/illo067b.png" alt="" width="350" height="81" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 38.</span> <span class="right49"><span class="smcap">Fig.</span> 39.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 38. and <span class="smcap">Fig.</span> 39.</p>
+</div>
+
+<div class="figcenter"><a name="Fig40" id="Fig40"></a>
+<img src="images/illo067c.png" alt="" width="150" height="84" />
+<p class="caption"><span class="smcap">Fig.</span> 40.</p>
+</div>
+
+<p>It should be noticed that rivets may, if in double shear,
+be loose in the middle thickness, due to enlargement of the
+hole in the central part and compression of the rivet, and
+yet show no sign of this by testing with the hammer. There
+is, however, generally marked evidence of another kind in<span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span>
+the &#8220;working&#8221; of the inner part, as, for instance, the web
+of a plate girder, in which case a discoloration due to rust is
+to be found along the edges of the angle bars, or a movement
+may be detected on the passage of live load. Red rust is, in
+fact, frequently an indication of something wrong, when no
+other evidence is apparent. In plate girders having <span class="lettsymb">T</span> or <span class="lettsymb">L</span>
+bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching
+these bars to the cross-girder tops loose, due to causes already
+dealt with. The riveted connection should, as to strength,
+bear some relation to the strength and stiffness of the parts
+secured, if the rivets are to remain sound.</p>
+
+<p>It may be well to give here a summarised statement of
+the results already named, for purposes of ready reference.
+These by themselves are not sufficient to enable working
+stresses to be deduced, though they are instructive. The<span class="pagenum"><a name="Page_57" id="Page_57">[57]</a></span>
+author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which
+the rivets behaved well, but is not now able to give precise
+particulars of these.</p>
+
+<p class="center"><span class="smcap">Examples of Rivet Stresses.</span></p>
+
+<table class="nowrap" summary="Table page 56">
+
+<tr class="bt bb">
+<th colspan="4" class="center br">&mdash;</th>
+<th class="center padl1 padr1 br">Span<br />in<br />Feet.</th>
+<th class="center padl1 padr1 br">Where<br />Found.</th>
+<th class="center padl1 padr1 br">Shear<br />Stress<br />in Tons<br />per<br />Square<br />Inch.</th>
+<th class="center padl1 padr1 br">Single<br />or<br />Double<br />Shear.</th>
+<th colspan="3" class="center padl1 padr1 br">Bearing<br />Pressure<br />in Tons<br />per<br />Square<br />Inch.</th>
+<th colspan="4" class="center padl1 padr1">Tight<br />or<br />Loose.</th>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="3" class="left padl1 padr1">Main girders</td>
+<td rowspan="3" class="right padr0 narrow">-</td>
+<td rowspan="3" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="3" class="narrow br">&nbsp;</td>
+<td class="center padl1 padr1 br">85</td>
+<td class="center padl1 padr1 br">Web</td>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="center padl1 padr1 br">D</td>
+<td rowspan="3" colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">11&middot;0</td>
+<td rowspan="3" colspan="3">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">66</td>
+<td class="center padl1 padr1 br">Diagonals</td>
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="center padl1 padr1 br">S</td>
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">63</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr2 br">14&middot;9</td>
+<td class="center padl1 padr1 br">S</td>
+<td class="right padl1 padr2 br">16&middot;3</td>
+<td class="left padr1">Tight generally.</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="4" class="left padl1 padr1">Small girders</td>
+<td rowspan="4" class="right padr0 narrow">-</td>
+<td rowspan="4" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="4" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">11</td>
+<td class="center padl1 padr1 br">Web</td>
+<td class="right padl1 padr2 br">1&middot;4</td>
+<td class="center padl1 padr1 br">D</td>
+<td rowspan="4" colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td rowspan="4" colspan="3" class="narrow">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">26</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">4&middot;3</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">24&middot;0</td>
+<td class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">11</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">7&middot;3</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">20&middot;6</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">11</td>
+<td class="center br">&#8222;</td>
+<td class="right padl2 padr1 br">9&middot;7</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">27&middot;4</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="3" class="left padl1 padr1">End connections</td>
+<td rowspan="3" class="right padr0 narrow">-</td>
+<td rowspan="3" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="3" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">27</td>
+<td class="center padl1 padr1 br">Ends</td>
+<td class="right padl1 padr2 br">5&middot;4</td>
+<td class="center padl1 padr1 br">S</td>
+<td colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;8</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td rowspan="2" class="center padl1 padr1 br">12</td>
+<td rowspan="2" class="center br">&#8222;</td>
+<td rowspan="2" class="right padl1 padr2 br">1&middot;8</td>
+<td rowspan="2" class="center padl1 padr1 br">D</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td class="right padl1 padr2 br">5&middot;8</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">8&middot;7</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl1 padr1">(Type case)</td>
+<td colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">26</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">4&middot;8</td>
+<td class="center padl1 padr1 br">S</td>
+<td colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+</table>
+
+<p>It is probable that the fact of a rivet being in single or
+in double shear largely affects its ability to resist the effects
+of bearing pressure, as commonly estimated. In the first
+case, the rivet-shank must bear heavily on the half-thickness
+of the plates or bars through which it passes, rather than on
+the whole thickness; and it is to be supposed that under
+this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.</p>
+
+<div class="figc400"><a name="Fig41" id="Fig41"></a><a name="Fig42" id="Fig42"></a>
+<img src="images/illo069.png" alt="" width="400" height="183" />
+<p class="caption_b"><span class="left43"><span class="smcap">Fig.</span> 41.</span> <span class="right56"><span class="smcap">Fig.</span> 42.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 41. and <span class="smcap">Fig.</span> 42.</p>
+</div>
+
+<p>The author has no very definite information in
+support of this contention, but suggests that for double
+shear the permissible bearing pressure may probably be as
+much as 50 per cent. greater than for rivets in single shear;
+the difference being made rather in the direction of increasing
+the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this
+is evident when it is considered that the practice has commonly
+been to make no distinction, so that whatever bearing
+pressures are found to be sufficient for both cases may be
+increased for those capable of taking the greater amount.
+<a href="#Fig41">Figs. 41</a> and <a href="#Fig42">42</a>, here given, illustrate the behaviour of rivets
+under the two conditions.</p>
+
+<p><span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span></p>
+
+<p>With reference to the amounts of the stresses to which
+rivets may be subject, the author concludes, as a result of his
+experience, coupled with a consideration of known laboratory
+tests, that for all dead load these may be quite prudently
+higher than is frequently taken. For iron the shear stress
+to be 10 per cent. less than the stress of parts joined; and
+the bearing pressure&mdash;for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary
+mild steel the shear stress to be 20 per cent. less than
+the stress in parts connected, and the bearing pressure equal
+to it for single-shear rivets; and 50 per cent. more for rivets
+in double shear, though the two latter values may probably
+approach those for wrought iron in steel of the higher grades
+sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction
+of the nominal working stress, arrived at by any one of the
+methods in use which may be adopted, affecting both the
+parts connected, and the rivets connecting them. For reverse
+stresses it is advisable to keep the shear stress in any
+rivet so low, say 3 tons per square inch, that the frictional
+resistance of the parts gripped by the rivets shall be sufficient
+to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure
+that, if brought to a bearing in one direction by the greater
+force, it shall not go back with reversal of stress. This requirement
+may be open to some question with respect to
+good machine-riveted work, but for hand-riveted connections
+it may certainly be adopted with wisdom.</p>
+
+<p>The following table will show at a glance how the stresses
+proposed vary with the unit stresses governing the main
+sections.</p>
+
+<p class="center"><span class="smcap">Proposed Table of Rivet Stresses.</span></p>
+
+<table class="nowrap" summary="Table page 58">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">Unit<br />Stress<br />in<br />Member.</th>
+<th class="center padl1 padr1 br">Shear<br />Stress.</th>
+<th class="center padl1 padr1 br">Bearing<br />Pressure<br />for<br />Single-Shear<br />Rivets.</th>
+<th class="center padl1 padr1">Bearing<br />Pressure<br />for<br />Double-Shear<br />Rivets.</th>
+</tr>
+
+<tr>
+<td colspan="4" class="center padl1 padr1 highline"><i>Wrought Iron.&mdash;Tons per Square Inch.</i></td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">3&middot;0</td>
+<td class="right padl1 padr2 br">2&middot;7</td>
+<td class="right padl1 padr4 br">3&middot;6</td>
+<td class="right padl1 padr4">5&middot;4</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr2 br">3&middot;6</td>
+<td class="right padl1 padr4 br">4&middot;8</td>
+<td class="right padl1 padr4">7&middot;2</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">5&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;5</td>
+<td class="right padl1 padr4 br">6&middot;0</td>
+<td class="right padl1 padr4">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">6&middot;0</td>
+<td class="right padl1 padr2 br">5&middot;4</td>
+<td class="right padl1 padr4 br">7&middot;2</td>
+<td class="right padl1 padr4">10&middot;8</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td class="right padl1 padr2 br">6&middot;3</td>
+<td class="right padl1 padr4 br">8&middot;4</td>
+<td class="right padl1 padr4">12&middot;6</td>
+</tr>
+
+<tr>
+<td colspan="4" class="center padl1 padr1 highline"><i>Steel.&mdash;Tons per Square Inch.</i></td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr2 br">3&middot;2</td>
+<td class="right padl1 padr4 br">4&middot;0</td>
+<td class="right padl1 padr4">6&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">5&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr4 br">5&middot;0</td>
+<td class="right padl1 padr4">7&middot;5</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">6&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;8</td>
+<td class="right padl1 padr4 br">6&middot;0</td>
+<td class="right padl1 padr4">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td class="right padl1 padr2 br">5&middot;6</td>
+<td class="right padl1 padr4 br">7&middot;0</td>
+<td class="right padl1 padr4">10&middot;5</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">8&middot;0</td>
+<td class="right padl1 padr2 br">6&middot;4</td>
+<td class="right padl1 padr4 br">8&middot;0</td>
+<td class="right padl1 padr4">12&middot;0</td>
+</tr>
+
+<tr class="bb">
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="right padl1 padr2 br">7&middot;2</td>
+<td class="right padl1 padr4 br">9&middot;0</td>
+<td class="right padl1 padr4">13&middot;5</td>
+</tr>
+
+</table>
+
+<blockquote>
+
+<p><span class="smcap">Note.</span>&mdash;Tension on rivets to be limited to one-half the permissible
+shear stress, the holes being slightly countersunk under snap-head.</p></blockquote>
+
+<p>It may be objected that the shear stresses in the proposed
+table are somewhat high for wrought iron and steel.
+This feature is intentional, and is supported by the consideration<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span>
+that whereas there may be loss of strength in the members
+of a structure by waste, there is no such loss in rivets,
+if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective
+field rivets is left to be dealt with as may be considered
+advisable for each particular case, the table as it stands being
+applicable only to riveting not below the standard of first-rate
+hand work.</p>
+
+<p>Cases of loose rivets in main girders over 50 feet span,
+due to any cause but bad work, are extremely rare, unless
+resulting from the action of some other part of the structure.
+It may be stated broadly that for railway bridges of less than
+perfect design, the nearer the rail, the more loose rivets,
+generally at connections. This is, no doubt, largely due to
+the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span>
+load, and because this effect has been but little modified by
+the elasticity of any considerable length of intervening girder-work.
+In addition to this, it is quite usual to find the rivets
+more heavily stressed, even though the load be considered
+as &#8220;static,&#8221; in the floor system than in the main-girders,
+though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting&mdash;viz., the
+connections&mdash;are commonly dealt with by hand; and for
+this reason it is the more necessary to design these with the
+greatest care.</p>
+
+<p>Any arrangement which favours the gradual acceptance
+of stress by one part from another will contribute to the
+integrity of riveted connections, and lessen the liability of
+the material to develop faults. In other branches of design
+this is well recognised, but appears in much old bridge work
+to have been entirely overlooked.</p>
+
+<p>Bridges carrying public roads very seldom furnish examples
+of loose rivets; the conditions are generally much
+more favourable, impact being practically absent, full loading
+infrequent, and the proportion of dead load to live, high.</p>
+
+<p>It is, perhaps, hardly necessary to insist upon rivets
+being, apart from mere considerations of strength, sufficiently
+near together to insure close work and exclude moisture.
+Outside edge seams should never be more widely spaced
+than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections,
+the greater stiffness of the section makes wider spacing
+allowable up to, say, 20 times the thickness; but this must
+be governed largely by the amount of riveting required to
+pull the parts close together. Where more than four thicknesses
+are to be gripped by the rivets, <sup>3</sup>&#8260;<sub>4</sub> inch in diameter is
+hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed <sup>5</sup>&#8260;<sub>8</sub> inch thick.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span></p>
+
+<h2>CHAPTER VI.<br />
+<span class="chaptitle">HIGH STRESS.</span></h2>
+
+<p>High stress, provided it be well below that at which immediate
+injury results, or possible failure, is not uniformly objectionable.
+It may be first considered relative to the absolute
+and elastic limits of strength, next with respect to the range
+of stress, and, finally, with regard to the frequency of application.
+For practical purposes&mdash;that is, for the continued
+efficiency of a structure&mdash;the limit of elasticity must be considered
+to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long
+as it lasts, be liable to the original measure of stress. There
+may be places in a bridge, however, over-stressed only in the
+earlier period of its existence, which, by being over-stressed
+and suffering deformation, permit the origin of this distortion
+to be harmlessly met in some other way. In such a
+case the injury done to that part does not, of necessity, lead
+to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail
+after being in use but a short time. As for riveting, so in
+dealing with the amount of stress to which a member is
+supposed to be liable, it should be clearly understood by what
+method this has been arrived at, whether the value assigned
+is the actual measure of the stress, or simply the conventional
+amount arrived at in the conventional way; perhaps neglecting
+web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal
+amount of stress, or including only a partial recognition of<span class="pagenum"><a name="Page_62" id="Page_62">[62]</a></span>
+those influences. In any case quoted the stress named is
+that at which the author arrives by the ordinary methods of
+computation carefully applied, where these appear to be
+sufficiently precise, unless any qualifying remark be added.
+Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that
+basis, and deducing the stress at the holes from the ratio of
+net to gross section at the extreme fibres; a method more
+correct than by reference to the moment of inertia of the net
+section. Any exhaustive refinement in the study of stresses
+is not attempted, both because it is beyond the author&#8217;s
+powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation
+in practice. Effective spans are taken at moderate
+values, and all exaggeration is avoided.</p>
+
+<p>The effects of impact in any part vary so much with
+nearness to, or remoteness from, the living load, and the
+frequency of development of the maximum stress from all
+causes acting together is so much affected by the same consideration,
+that it is apparent a nominal stress which may be
+harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as
+ordinarily stated&mdash;i.e., at so much per square inch, uniform
+across a section&mdash;is seldom a cause of trouble. In nearly all
+cases of failure there is an accompanying localised destructive
+stress, either in rivets or elsewhere, with crippling or deformation
+of some essential part. In the tension flanges of main
+girders with uncomplicated stress, this may run up to an
+amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the
+compression flanges, if these be in themselves sufficiently
+stiff, or properly restrained from side flexure. In support of
+the above statement may be quoted the following instances
+relating to wrought-iron structures<span class="nowrap">:&mdash;</span></p>
+
+<p><span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span></p>
+
+<p>A bridge of 60 feet effective span, having girders
+immediately under the rails, had a flange stress of 6&middot;3 tons
+per square inch. Another of 64 feet span, carrying two lines
+of way, with outside main girders and cross-girders, had the
+flanges of the former stressed to 6&middot;8 tons per square inch.
+A third, of 76 feet span, of similar construction to the last,
+was stressed in the main girder flanges to 7&middot;5 tons per square
+inch. The webs were not included in the computation; the
+figures, therefore, compare with ordinary practice. In these
+three cases the main girders showed no signs of distress,
+referable to the results stated, though the top flanges in the
+last case were curved inwards. The effect of this flexing of
+the flange would be, of course, to increase the amount of
+compressive stress along one edge, though to what degree
+cannot now be stated.</p>
+
+<div class="figc600"><a name="Fig43" id="Fig43"></a><a name="Fig45" id="Fig45"></a><a name="Fig44" id="Fig44"></a>
+<p class="caption"><span class="smcap">Fig.</span> 43.</p>
+<img src="images/illo076.png" alt="" width="600" height="308" />
+<p class="caption_b"><span class="left70"><span class="smcap">Fig.</span> 44.</span> <span class="right29"><span class="smcap">Fig.</span> 45.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 44. and <span class="smcap">Fig.</span> 45.</p>
+</div>
+
+<p>A further instance of considerable flange stress occurred
+in a bridge of seven nearly equal continuous spans, 25 feet
+generally, the end and greatest span being 29 feet 6 inches,
+centre to centre of bearings. Some details of the bridge are
+given in <a href="#Fig43">Figs. 43 to 45</a>. The four inner main girders
+under rails were 2 feet deep, with webs <sup>1</sup>&#8260;<sub>2</sub> inch thick over
+piers, and <sup>3</sup>&#8260;<sub>8</sub> inch at abutments, having flanges of two <span class="lettsymb">L</span> bars,
+3 inches by 3 inches by <sup>5</sup>&#8260;<sub>8</sub> inch. There were also two
+outer girders of the same depth, with single <span class="lettsymb">L</span> bars. Plate
+diaphragms of full girder depth and particularly stiff were
+carried right across the bridge at the centre of the spans,
+and over the piers. The girders, though evidently designed
+to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see <a href="#Fig45">Fig. 45</a>).
+It is doubtful if the girders acted with strict continuity for
+long after erection, as the excessive stress in the rivets of the
+flange joint would, for that condition, have been nearly
+sufficient to shear them. It is probable that this being so,
+the joints first yielded, relieving the bending moment over<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span>
+the piers, and increasing it near mid-span. Whether the end
+spans be considered as strictly continuous with the rest, or
+as simple beams, the maximum bending moments would not<span class="pagenum"><a name="Page_65" id="Page_65">[65]</a></span>
+greatly differ, though occurring for continuity over the pier,
+for free beams at the centre. There is, however, an intermediate
+condition which makes the moments at these two
+places less than either maximum, but equal to each other;
+a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been
+calculated, giving the minimum stress value that can be
+accepted. The diaphragm has been assumed to transfer to
+the outer girders a due proportion of the load. With this
+explanation it may now be stated that, under engine loads
+corresponding to those running, the flange stress worked out
+at 7&middot;4 tons per square inch tension, web included, or 9&middot;7
+tons per square inch without considering the web; which
+stresses, it is more than probable, may have been greater.
+The figures include the consideration of anything which may
+contribute to lowering the stress, and are hardly to be compared
+with those worked to in ordinary design of new work,
+in which it would be quite usual to neglect the assistance of
+the outer girders and the webs, to work to heaviest engine-loads,
+and possibly include an allowance for the effects of
+settlement. Dealt with in this way the girders would seem
+to be of about one-fourth the strength that would be required
+in the design of a new bridge, in which certain elements of
+strength would be deliberately ignored.</p>
+
+<p>The ironwork was in good condition, there was no ordinary
+evidence of weakness apart from the calculated results,
+the vibration was distinctly moderate, and the deflection,
+though not recorded, was certainly small. The bridge did,
+indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long
+overstressed may have a sensibly higher modulus of elasticity
+than newer work at more moderate stresses. The traffic was
+not very considerable, and both roads, of the same spans,
+but seldom loaded at the same time; though with this construction<span class="pagenum"><a name="Page_66" id="Page_66">[66]</a></span>
+of bridge there would in either case be very little
+difference. The author recalls no reason for supposing that
+the piers had yielded in any sensible degree. The bridge
+was rebuilt after some thirty-six years&#8217; use.</p>
+
+<p>Stress of considerable amount in the flanges of a latticed
+main girder of 63 feet span has already been noticed in the
+chapter on &#8220;<a href="#Page_45">Riveted Connections</a>,&#8221; which for the tension
+boom worked out to 7&middot;1 tons per square inch, the flanges
+in this case showing no signs of weakness. An instance has
+also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons
+per square inch, the girder recovering its form when relieved
+of load.</p>
+
+<p>As to stress in cross-girder flanges, an example may be
+quoted of a bridge of 109 feet span, carrying two roads,
+having outside main girders, with cross-girders between;
+these latter were stressed in the flanges to 6&middot;7 tons per
+square inch (webs not included), if the partial distribution
+among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some
+reason to think in this instance that distribution had the
+effect of reducing the stress quoted, as the observed deflection
+of the cross-girders was materially less than that calculated
+for girders acting independently of each other, though
+this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the
+heavy main girders, would also tend to moderate the stress.
+No very definite conclusion can therefore be deduced from
+this instance.</p>
+
+<p>To take another case of less uncertainty, the bridge of
+35 feet span (see <a href="#Fig33">Fig. 33</a>), referred to in &#8220;<a href="#Page_45">Riveted Connections</a>,&#8221;
+may again be cited. The extreme fibre stress in the
+cross-girder flanges worked out at 6&middot;3 tons per square inch,
+web included, or 6&middot;5 tons, exclusive of the web. It cannot<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span>
+be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was <sup>1</sup>&#8260;<sub>2</sub> inch on the
+span of 11 feet, in addition to a permanent set of <sup>3</sup>&#8260;<sub>4</sub> inch,
+largely due, however, to &#8220;working&#8221; rivets.</p>
+
+<p>A better and altogether conclusive case of the way in
+which cross-girders may occasionally suffer considerable
+stress, and show no sign, is furnished by two cross-girders,
+of which some particulars are here given. These girders
+occurred in the floor of a very acute angled skew bridge,
+riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end
+on a masonry abutment. The first girder was about 19 feet
+effective span, 12 inches deep in the web, with angle bar and
+plate flanges. The girders were spaced 6 feet apart, and
+were connected under the rails by <span class="lettsymb">T</span>-bars, cranked down to
+face the webs, and riveted through. Though these <span class="lettsymb">T</span>&#8217;s had
+little stiffness, yet the frequent vertical movements of the
+girders relative to each other, under passing loads, had broken
+the majority of the <span class="lettsymb">T</span>-bars at the bends, so that no notice
+need be taken of these as transferring load from any one
+cross-girder to its neighbour. The floor covering consisted
+of timbers about 4 inches thick, also incompetent to transfer
+any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers,
+chairs, and ordinary bull-headed rails. The stress to which
+the girder was liable works out at 8&middot;4 tons per square inch,
+on the extreme fibres of the net section, web included; or
+9&middot;1 tons, neglecting the web, under engine-loads of a
+common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with
+angle bar and plate flanges. The stress per square inch was
+10&middot;5 tons, web included, or 11&middot;1 tons per square inch,
+neglecting the web. This girder carried three rails, one of
+which was near to the abutment bearing, so that there was<span class="pagenum"><a name="Page_68" id="Page_68">[68]</a></span>
+no great difference in the stress induced whether all three rails
+were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a
+common occurrence for the girders to take the full loads.
+The heavier engines passed scores of times in a day&mdash;lighter
+engines probably one hundred times. The bridge was about
+twenty years old, yet these cross-girders, when removed,
+showed no other sign of age and wear than that due to rust.</p>
+
+<div class="figcenter"><a name="Fig46" id="Fig46"></a>
+<img src="images/illo080.png" alt="" width="500" height="241" />
+<p class="caption"><span class="smcap">Fig.</span> 46.</p>
+</div>
+
+<p>All the foregoing instances relate to wrought-iron bridges.
+Two cases of steel construction are here added, the first of
+these furnishing an example of high girder stress somewhat
+remarkable. This was found in a trough girder of a strange
+pattern, of which a section is here given (<a href="#Fig46">Fig. 46</a>). The
+bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a
+crawling pace. The larger of the two girders carrying the
+rails was 15 feet 8 inches effective span. The sides of the
+trough consisted each of two vertical plates, originally <sup>1</sup>&#8260;<sub>2</sub> inch
+thick, but wasted to an aggregate thickness of <sup>5</sup>&#8260;<sub>8</sub> inch.
+These plates 6 inches deep, were connected at their lower
+edges to angle bars, 3 inches by 3 inches by <sup>1</sup>&#8260;<sub>2</sub> inch, which
+again were riveted to a bottom plate 16 inches wide,
+originally <sup>1</sup>&#8260;<sub>2</sub> inch thick, wasted to <sup>3</sup>&#8260;<sub>8</sub> inch. Lying in the bottom<span class="pagenum"><a name="Page_69" id="Page_69">[69]</a></span>
+of the trough, and riveted through the inner angle flanges,
+was a bridge-rail. Assuming that the metal retained its
+elastic properties from top to bottom of the section, at
+whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the
+net section. As puddled steel, of which the girders were
+made, may have a tenacity of 45 to 55 tons per square inch,
+the assumption is probably correct. The author has no
+record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine
+passing over, required some determination.</p>
+
+<p>A point of additional interest in this little bridge is that,
+though made of steel, it dates as far back as 1861, having
+been in use thirty-two years when removed. The particular
+variety of steel used was known as Firth&#8217;s puddled. The
+evidence of this consists in correspondence showing that permission
+had been asked of the controlling authority, by the
+only users of the siding, to apply this material, with no evidence
+of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some
+girders of considerable span. The appearance of the trough
+girders to which the foregoing particulars apply was distinctly
+different to that which might be expected in ordinary
+wrought iron. The top edges of the vertical plates were
+wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which
+the girders held up to their work for so long is, by itself,
+conclusive on the point. The bridge-rail appeared to be of
+wrought iron, the different modulus of elasticity of which
+has been included in the calculation upon which the preceding
+results are based. That these girders stood so well is,
+perhaps, largely due to the fact that the load carried by them
+was, though varying within wide limits, practically free from
+impact, which, had the load passed over quickly, would, with<span class="pagenum"><a name="Page_70" id="Page_70">[70]</a></span>
+girders so small, shallow and flexible, have been very sensible.</p>
+
+<p>The second instance of steel construction in which somewhat
+high stress is manifest is that of some steel troughing of
+the Lindsay pattern, used in a bridge built in 1885. The
+troughs ran parallel to the rails, having an effective span of
+18 feet 8 inches. The depth of the section (which is shown
+in <a href="#Fig47">Fig. 47</a>), was 8<sup>1</sup>&#8260;<sub>2</sub> inches, making a ratio of depth to span
+of <sup>1</sup>&#8260;<sub>28</sub>. The road was of ballast, sleepers, chairs, and 85-lb.
+rails.</p>
+
+<div class="figcenter"><a name="Fig47" id="Fig47"></a>
+<img src="images/illo082.png" alt="" width="400" height="208" />
+<p class="caption"><span class="smcap">Fig.</span> 47.</p>
+</div>
+
+<p>Assuming this to be carried on six troughs, which corresponds
+to 11 feet 3 inches of width, the extreme fibre stress
+works out at 7&middot;5 tons per square inch, under usual engine-loads.
+The bridge when examined after fourteen years&#8217; use was
+in good condition, and at that time but little rusted; but the
+end seam rivets were, as is not uncommon with such troughing,
+loose. The traffic over the bridge was considerable, but
+not at great speed.</p>
+
+<p>On the opposite page are set out the results which have
+been given, in tabulated form, as was done for rivet stresses,
+to enable ready comparison to be made.</p>
+
+<p class="center"><span class="smcap">Examples of High Stress.</span><span class="pagenum"><a name="Page_71" id="Page_71">[71]</a></span></p>
+
+<table class="nowrap" summary="Table page 71">
+
+<tr class="bt bb">
+<th rowspan="2" colspan="3" class="center padl1 padr1 br">&mdash;</th>
+<th rowspan="2" colspan="4" class="center padl1 padr1 br">Span<br />in<br />Feet.</th>
+<th rowspan="2" class="center padl1 padr1 br">Part<br />Stressed.</th>
+<th colspan="2" class="center padl1 padr1 br">Stress per<br />Square Inch.</th>
+<th rowspan="2" class="center padl1 padr1 br">Tension<br />or<br />Compression.</th>
+<th rowspan="2" colspan="4" class="center padl1 padr1">Condition.</th>
+</tr>
+
+<tr class="bb">
+<th class="center padl1 padr1 br">Webs<br />Included.</th>
+<th class="center padl1 padr1 br">Webs not<br />Included.</th>
+</tr>
+
+<tr>
+<td class="center padl1 wrappable">Wrought-iron</td>
+<td class="center wrappable">main girders,</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">60&middot;0</td>
+<td rowspan="3" colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">Flange</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td rowspan="3" colspan="3">&nbsp;</td>
+<td class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">64&middot;0</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;8</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">76&middot;0</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">7&middot;5</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td rowspan="2" class="center">&#8222;</td>
+<td rowspan="2" class="center">&#8222;</td>
+<td rowspan="2" class="center br">&#8222;</td>
+<td rowspan="2" class="right padl1 padr1">29&middot;5</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="2" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr3 br">7&middot;4</td>
+<td class="right padl1 padr3 br">9&middot;7</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="right padl1 padr3 br">8&middot;3</td>
+<td class="center padl1 padr1 br">Compression</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="left padl1 padr1 br">lattice</td>
+<td class="right padl1 padr1">63&middot;0</td>
+<td rowspan="6" colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td colspan="2" class="center padl1 padr1 br">7&middot;1</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td rowspan="6" colspan="3">&nbsp;</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">47&middot;0</td>
+<td class="center padl1 padr1 br wrappable">Flange edge</td>
+<td class="right padl1 padr3 br">10&middot;0</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">Compression</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center padl1 wrappable">Wrought-iron</td>
+<td class="center wrappable">cross-girders,</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">26&middot;0</td>
+<td class="center padl1 padr1 br">Flange</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;7</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">11.0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="right padl1 padr3 br">6&middot;5</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Bad; loose rivets.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">19&middot;0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">8&middot;4</td>
+<td class="right padl1 padr3 br">9&middot;1</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Good, but rusted.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">22&middot;0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">10&middot;5</td>
+<td class="right padl1 padr3 br">11&middot;1</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Good, but rusted.</td>
+</tr>
+
+<tr>
+<td rowspan="2" colspan="3" class="left padl1 padr1 br">Steel trough girder</td>
+<td rowspan="2" class="right padl1 padr1">15.7</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="2" class="br narrow">&nbsp;</td>
+<td class="center br">&#8222;</td>
+<td colspan="2" class="center br">15&middot;0</td>
+<td class="center br">&#8222;</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1 wrappable">Fair, but rusted.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br wrappable">Top edge</td>
+<td colspan="2" class="center br">32&middot;0</td>
+<td class="center br">Compression</td>
+</tr>
+
+<tr class="bb">
+<td colspan="3" class="left padl1 padr1 br">Steel troughing</td>
+<td class="right padl1 padr1">18&middot;7</td>
+<td colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">Flanges</td>
+<td class="right padl1 padr3 br">7&middot;5</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br wrappable">Tension and Compression</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Fair, but rusted.</td>
+</tr>
+
+</table>
+
+<p>It would be unwise to infer from the instances which<span class="pagenum"><a name="Page_72" id="Page_72">[72]</a></span>
+have been quoted that high stress may be regarded with
+complaisance. In the most conscientious engineering work
+there should still be a liberal margin for material possibly
+defective, or even bad, for waste and deterioration, and for
+the aggregate effect of minor errors in design, any one of
+which considerations, except the first, by itself might not be
+of great importance. The conclusion which may, however,
+be derived from this and the previous chapters is, that bridge
+failures are less likely to occur from high stress of a kind
+readily calculated than from failure in detail, obscure and
+little suspected, the reason for which is not perhaps apparent,
+till the attention is forcibly directed to it by the refusal of
+the structure to sustain the forces to which it may be liable.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_73" id="Page_73">[73]</a></span></p>
+
+<h2>CHAPTER VII.<br />
+<span class="chaptitle">DEFORMATIONS.</span></h2>
+
+<p>Instructive lessons are to be had from a study of the
+various alterations in form to which metallic bridgework is
+liable, which alterations may be due simply to the development
+of stress of ordinary amount, and are then generally
+small; or to abnormal stresses, the result of some distortion
+in the bridge structure itself not originally intended, and
+possibly extreme. In addition to these there may be deformations
+due to settlement, to &#8220;creeping&#8221; of parts of the
+structure relative to the rest, to temperature changes, to rust,
+and to original bad workmanship. In any instance quoted
+below the methods adopted to ascertain the amounts of such
+alterations were quite simple, even crude; but as care was
+exercised, and no attempt made to measure any very minute
+changes, the results may be accepted as practically correct.</p>
+
+<p>Dismissing for the present changes of form such as are
+to be expected, and touched upon in other places in this
+work, with respect to the particular parts of bridge structures
+affected by them, a few instances will be adduced of
+alterations which, though not very surprising, are such as in
+the design of the work are hardly likely, in most instances,
+to have been contemplated.</p>
+
+<p>A case has already been referred to in which, owing to
+eccentric loading of main girders, these were, as to the top
+flanges, flexed sideways a considerable amount. It is proposed
+to supplement this by further remarks relative to
+somewhat similar cases. A like effect is frequently to be<span class="pagenum"><a name="Page_74" id="Page_74">[74]</a></span>
+observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting
+ledges formed by the bottom angle-bars of such troughs.
+In old forms of this arrangement it is common to find the
+two girders forming the trough connected only by bolts
+passing through the timbers, or just above them and below
+the rails; or connected by narrow strips, which serve no
+other purpose than to prevent the sides spreading at the
+bottom. The top flanges in such cases commonly curve
+inwards on the passage of the running load, accompanied of
+necessity by an increase of compressive stress upon the outer
+edges of the flanges, and perhaps by the working of any
+flange-joint which may exist. This, both as to flexing of
+the top flange and the working of a joint, was noticed in
+the case of a bridge twenty-three years old, very similar to
+that illustrated in <a href="#Fig8">Figs. 8</a> and <a href="#Fig9">9</a>, and described on <a href="#Page_13">pages 13</a>
+and <a href="#Page_14">14</a>. The top flange consisted, however, of a bridge rail
+riveted to the top edge of the web, butting at a joint, and
+covered by thick cover strips (see <a href="#Fig48">Fig. 48</a>). The joint itself
+was poor, and depended largely upon the character of the
+butt, which was not sufficiently good to prevent the top
+member kinking at this point, under the joint influence of
+transverse effort and compressive stress, with possibly some
+help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked
+in passing that it is very objectionable to use bolts as was
+done in this instance; for as the timber settles down on its
+seat, taking the bolts with it, these bear hard in the webs,
+enlarging or even, as in this case, tearing the holes, accompanied
+by injury to the bolts themselves. The practice is
+now almost obsolete, but the example is instructive as showing
+the impropriety of securing timbers by bolts passing through
+them at right angles to the action of the load, unless these
+bolts are quite free to move with the timber as it compresses.</p>
+
+<p><span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span></p>
+
+<p>If trough girders must be used, the better plan is to
+connect the two sides by a continuous bottom plate, the
+trough thus formed being properly drained, if the timber
+is not bedded in asphalt concrete; or to introduce stiff
+diaphragms at intervals beneath timbers, if the depth
+suffices.</p>
+
+<p>In the case just quoted the curvature of the top members
+of the girders was inwards, but in the instance given below,
+of twin girders 26 feet effective span, with longitudinal
+timbers between, resting, as before, upon the inner ledge
+formed by the bottom flanges, the curvature was observed in
+three out of four girders to be <sup>1</sup>&#8260;<sub>2</sub> inch in a contrary direction,
+the fourth remaining straight.</p>
+
+<div class="figc450"><a name="Fig48" id="Fig48"></a><a name="Fig49" id="Fig49"></a>
+<img src="images/illo087.png" alt="" width="450" height="201" />
+<p class="caption_b"><span class="left35"><span class="smcap">Fig.</span> 48.</span> <span class="right64"><span class="smcap">Fig.</span> 49.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 48. and <span class="smcap">Fig.</span> 49.</p>
+</div>
+
+<p>An inspection of the accompanying section, <a href="#Fig49">Fig. 49</a>, will,
+perhaps, render the reason evident when it is noticed that
+the top members are very unsymmetrical in form, the effect
+of this being to give these members, under stress, a strong
+tendency to flex outwards, apparently more than sufficient
+to counteract the tendency of an eccentric application of
+load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be
+not materially in excess, and is actually so, only because the
+thinness of the web&mdash;<sup>1</sup>&#8260;<sub>4</sub> inch&mdash;renders it incompetent to keep
+the bottom flange up to its work, and so secure the full
+effect of the eccentric loading in limiting the outward tendency,<span class="pagenum"><a name="Page_76" id="Page_76">[76]</a></span>
+due to the section of the top member, the effects of
+which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange
+to the other prevent the want of symmetry noticed in these&mdash;which,
+by the way, is on the wrong side for utility&mdash;from
+having any particular effect.</p>
+
+<p>To give one other example of the consequences of eccentric
+loading, a bridge of 48 feet effective span may be quoted.
+This bridge carried four lines of way supported by five main
+girders, trussed by kicking-struts in such a manner as to form
+a bastard arch. A part section and plan are given in <a href="#Fig50">Figs.
+50</a> and <a href="#Fig51">51</a>.</p>
+
+<div class="figcenter"><a name="Fig50" id="Fig50"></a>
+<img src="images/illo089a.png" alt="" width="450" height="482" />
+<p class="caption"><span class="smcap">Fig.</span> 50.</p>
+</div>
+
+<div class="figcenter"><a name="Fig51" id="Fig51"></a>
+<img src="images/illo089b.png" alt="" width="500" height="198" />
+<p class="caption"><span class="smcap">Fig.</span> 51.</p>
+</div>
+
+<p>The floor consisted of Lindsay&#8217;s troughing resting upon
+the lower flanges of the main girders, the three middle
+girders, subject to eccentric loading, sometimes on one side,
+sometimes on the other, were, with dead load only, straight;
+but the two outer girders, liable to loading only on one side,
+had, under repeated applications of such a load, assumed a
+permanent curve towards the rails&mdash;<sup>13</sup>&#8260;<sub>16</sub> inch in one case and
+1 inch in the other&mdash;which curvature, no doubt, increased
+when a live load came upon the contiguous roads, though
+this was not measured. It should be remarked in passing
+that, owing to settlement and the canting of the abutments,
+the three middle girders were also &#8220;down&#8221;&mdash;in one case <sup>3</sup>&#8260;<sub>4</sub>
+inch. The girders, with one near road loaded, deflected <sup>1</sup>&#8260;<sub>8</sub> inch&mdash;greatly
+less than would have been the case had the main
+girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.</p>
+
+<p>Deformations due to settlement may be very considerable.
+The author recalls two instances affecting continuous girders.
+In the first of these, a bridge twenty years old, of two spans
+of about 50 feet each, and with girders 4 feet 6 inches deep,
+the centre pier had sunk 4 inches, reducing the spans, as
+respects the dead load, practically to the condition of simple<span class="pagenum"><a name="Page_77" id="Page_77">[77]</a><br /><a name="Page_78" id="Page_78">[78]</a></span>
+beams, just resting, but hardly bearing, upon the piers when
+free of live load.</p>
+
+<p>In the second case, also of two openings of about 55 feet
+each, with girders 8 feet deep, one abutment had sunk about
+3 inches, more than doubling the stresses over the centre
+pier. It is manifest that continuous girders should only be
+adopted where settlement of the supporting points is not
+likely to occur to any material degree. If this cannot be
+relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to
+make a liberal allowance for settlement stresses, in which
+case any economical advantage that should exist will probably
+disappear. It is, however, to be acknowledged that so long
+as the girders are in touch, under dead load, with the bearings
+intended to support them, the stresses due to a live load
+are unaltered, the principal effect in this case being that the
+variation in stress due to the live load ranges between limits
+that are higher or lower in the scale of stress than is the
+case with bearings undisturbed; still, if it is desired that
+the maximum stress shall not exceed, say, 6 tons per square
+inch, it can hardly be a matter of indifference that settlement
+shall induce a maximum of, perhaps, 10 tons, as in that case
+the stress must be 4 tons nearer the limit of statical strength.</p>
+
+<p>Before leaving this matter it may be well to point out
+that in the case of continuous girders of uniform section a
+moderate settlement of the piers may even be advantageous
+by reducing the moments over the piers, and possibly making
+them equal to those obtaining near the middle of the spans,
+in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.</p>
+
+<p>Bridges consisting of simple main girders connected by
+cross-girders may be very prejudicially affected by unequal
+settlement; for instance, if one girder bearing settles more
+than the others, a twist is put upon the structure very trying<span class="pagenum"><a name="Page_79" id="Page_79">[79]</a></span>
+to the floor-girder connections, and possibly to the main
+girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments.
+Indeed, settlement of this kind may be much more destructive
+to a metallic bridge than to an arch of brick or masonry,
+the commonly accepted opinion notwithstanding.</p>
+
+<p>Instances of deformations due to the creeping of some
+part of the structure away from its work, are within the
+author&#8217;s knowledge, rare; except in the case of the ends of
+main girders in skew bridges, already referred to.</p>
+
+<p>Distortion, the result of temperature changes, is frequently
+to be observed in any considerable length of girder
+flange or parapet where there is not freedom of movement,
+unless due provision is made to check it.</p>
+
+<p>It is quite common to see parapets out of line, either
+because the ends are not free, or because the light work of
+the parapet being more exposed to the sun&#8217;s rays than the
+girder work to which the lower part is attached, expanding
+to a greater degree, is subject to considerable compressive
+force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or
+flexible joints at moderate distances apart, or to make the
+parapet sufficiently stiff to take the stresses developed, without
+crippling. A parapet may also go out of shape if directly
+attached to the top flange of a girder liable to heavy loading,
+particularly if the girder be shallower than the parapet,
+simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the
+girder proper.</p>
+
+<p>Rivets spaced too far apart, by allowing the plates or
+other parts to spring open slightly, and permitting moisture
+to enter, results in the growth of rust, which, as it swells in
+forming, forces the parts asunder, and may set up considerable
+stress.</p>
+
+<p><span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span></p>
+
+<p>Flat bars riveted together by rivets spaced 12 inches
+apart may from this cause be forced asunder, as much as <sup>1</sup>&#8260;<sub>2</sub>
+inch, sufficient to set up a stress, with any practicable thickness
+of bar, much exceeding the elastic limit.</p>
+
+<p>Local distortions may occur as the result of imperfect
+workmanship or careless erection, causing quite possibly very
+severe local stresses; or girder flanges may be out of straight
+as a result of riveting up along one side first, instead of
+advancing the riveting simultaneously along the whole
+breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is
+sometimes done to girderwork during manufacture by rough
+treatment to make the work come together; but the author
+has little to offer with respect to these matters that is not
+common knowledge. It may, however, be pointed out in
+passing that a bridge upon the design of which great care
+has been expended, with the idea that theoretical propriety
+shall not be violated, may be completely spoiled in this
+respect by careless construction. Fortunately, both steel
+and wrought iron, if of good quality, are long suffering.
+Incompetent erection will sometimes result in the true girder
+camber not appearing, or in differences as between girders
+supposed to be similar. This is not, of course, a deformation
+in the sense in which the word has previously been used, but
+it is desirable to bear the fact in mind as a possible cause of
+defective camber in dealing with questions of deformation.</p>
+
+<p>The foregoing has reference chiefly to alterations of form
+in bridgework of wrought iron or steel, but a case of considerable
+interest is that of a cast-iron arched structure, of
+which the author made a very complete examination.</p>
+
+<div class="figcenter"><a name="Fig52" id="Fig52"></a>
+<img src="images/illo093a.png" alt="" width="600" height="119" />
+<p class="caption"><span class="smcap">Fig.</span> 52.</p>
+<p class="largeimg"><a href="images/lg093a.png">Large image</a> (41 kB)</p>
+</div>
+
+<div class="figcenter"><a name="Fig53" id="Fig53"></a>
+<img src="images/illo093b.png" alt="" width="600" height="157" />
+<p class="caption"><span class="smcap">Fig.</span> 53.</p>
+</div>
+
+<p>This bridge, built in 1839, and carrying two lines of
+railway, consisted of three spans, 100 feet each, of 10 feet
+rise, made up of four inner and two outer ribs, each rib
+being in three nearly equal parts; the floor was of timber,<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span>
+the abutments and piers of masonry. As originally constructed
+there was no bracing between the ribs other than
+the frames indicated on the plan here given (<a href="#Fig52">Fig. 52</a>),<span class="pagenum"><a name="Page_82" id="Page_82">[82]</a></span>
+stretching from outer rib to outer rib in the neighbourhood
+of the rib joints, which were simple butts without bolts or
+any equivalent means of connection. The floor was, however,
+braced in the horizontal plane, and the structure was
+also braced over the masonry piers. After forty-two years&#8217;
+use supplementary distance-pieces were introduced between
+the ribs, but still no bracing between them, or any efficient
+means of checking lateral movement. A crack developing
+in one of the outer ribs at the crown, led to an investigation
+to trace the cause, the bridge then being fifty-four years old.
+Careful plumbing of the abutments revealed the fact that
+three out of four abutment pilasters were out of the vertical,
+as shown in <a href="#Fig52">Figs. 52</a> and <a href="#Fig53">53</a>, the greatest amount being
+<sup>5</sup>&#8260;<sub>8</sub> inch in 6 feet&mdash;at that corner from which the cracked rib
+had its springing; there was also other evidence of settlement
+in an old crack extending from the top of the abutment
+to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were
+also out of plumb, that which was cracked being 2<sup>1</sup>&#8260;<sub>2</sub> inches
+out at the centre. The joints of the ribs, which, as already
+stated, were simple butts, in some cases opened and shut, as
+the load passed over, in such a way as to suggest that the
+ribs were acting, in a manner, as four-hinged arches, of
+which two hinges were at the springing, and the other two
+at the joints, one of which would for most positions of the
+load be out of use, reducing the rib to the three-hinged condition;
+in other words, as the rolling load passed over the
+span, one or other of the two joints of a rib would &#8220;gape&#8221;
+an appreciable amount at the bottom or at the top. Observations
+were taken by means of a theodolite placed below,
+either upon the bank or upon the tops of the masonry piers,
+sighting upon suitable scales attached to the ribs to ascertain
+the amounts of vertical and horizontal movement during the<span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span>
+passage of trains over the bridge. The principal results are
+set forth in the following table<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Movements of Cast-Iron Ribs under Live Load in a Bridge<br />
+of Three 100-Ft. Spans.</span></p>
+
+<table class="nowrap" summary="Table page 83">
+
+<tr class="bt bb">
+<th colspan="3" class="center padl1 padr1 br">&mdash;</th>
+<th class="center padl1 padr1 br">Fall<br />in<br />Inches.</th>
+<th class="center padl1 padr1 br">Rise<br />in<br />Inches.</th>
+<th class="center padl1 padr1">Lateral<br />Movement<br />in Inches.</th>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 1.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">A.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;20</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1">&middot;04</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">A.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1 br">&middot;03</td>
+<td class="center padl1 padr1">&middot;04</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">B.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;14</td>
+<td class="center padl1 padr1 br">No record.</td>
+<td class="center padl1 padr1">&middot;02</td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 2.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">C.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;40</td>
+<td class="center padl1 padr1 br">&middot;13</td>
+<td class="center padl1 padr1">Slight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">C.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;10</td>
+<td class="center padl1 padr1 br">&middot;05</td>
+<td class="center padl1 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 3.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">D.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;22</td>
+<td class="center padl1 padr1 br">No record.</td>
+<td class="center padl1 padr1">No record.</td>
+</tr>
+
+<tr class="bb">
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">D.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;15</td>
+<td class="center padl1 padr1 br">Slight.</td>
+<td class="center padl1 padr1">Slight.</td>
+</tr>
+
+</table>
+
+<blockquote>
+
+<p><span class="smcap">Note.</span>&mdash;The lateral movements are to either side of the mean
+position.</p></blockquote>
+
+<p>The particulars for spans 2 and 3 were obtained with
+the instrument set up on the pier between these spans. The
+tremor of this pier was such that no useful readings for
+lateral movement could be obtained. Further, as the rolling
+load came upon these spans, the effect was to rock the pier
+to an extent vitiating the readings for vertical displacement;
+but by sighting upon the fixed abutment, and observing the
+amount of this rocking, suitable corrections were made in
+the apparent rib movements. The figures given in the table
+are thus corrected. The pier rocking was equivalent, as an
+extreme, to an inclination from the vertical of 1 in 3200.
+An attempt to measure the horizontal movement of the pier-top<span class="pagenum"><a name="Page_84" id="Page_84">[84]</a></span>
+was unsuccessful, owing to the impracticability of setting
+up the instrument in a suitable position, sufficiently near to
+the pier to enable readings to be satisfactorily taken. This
+horizontal displacement probably amounted to about <sup>1</sup>&#8260;<sub>16</sub> inch
+either way. The rise and fall of the arches, and rocking
+either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect
+to the spans. Summarising the results, the greatest vertical
+movements downwards were 0&middot;20 inch, 0&middot;40 inch, and 0&middot;22
+inch for spans Nos. 1, 2, and 3, the upward movements being
+0&middot;08 inch and 0&middot;13 inch for the first and second spans,
+there being no recorded result of this kind for the third
+span. With adjacent ribs loaded, the movement of the
+ribs unloaded was one from one-third to one-half of the full
+amounts. It is to be noted that the lateral displacement in
+no case exceeded 0&middot;04 inch either way, nor were the vertical
+movements exceptional; yet, as a matter of sensation, when
+seated upon the ironwork, it was a little difficult to believe
+them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0&middot;45
+inch, 0&middot;45 inch, and 0&middot;55 inch for the spans in order, the
+extreme temperatures being fairly representative of the
+English winter and summer. The structure was, as a consequence
+of the examination, efficiently braced by diaphragms
+between the ribs, and diagonals following the arch ribs round
+from springing to springing, with satisfactory results. The
+crack already referred to, and its probable causes, will be
+dealt with under &#8220;<a href="#Page_141">Cast-Iron Bridges</a>.&#8221; Eventually this
+bridge was reconstructed to meet the requirements of growing
+engine-loads.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span></p>
+
+<h2>CHAPTER VIII.<br />
+<span class="chaptitle">DEFLECTIONS.</span></h2>
+
+<p>Deflection, considered only as a fraction of the span, and
+without regard to other conditions affecting it, is of very
+little use as an indication of a girder&#8217;s fitness for its work;
+but when taken with reference to the depth of the girder,
+the nature and amount of the load producing flexure, and,
+further, with regard to the quality of the workmanship and
+normal properties of the material of which the beam is constructed,
+it may be of some little service in helping to form
+a reliable opinion. This consideration applies with less
+force, perhaps, to new work than to old, in which there may
+be unknown influences at work, or unknown defects which
+by excessive deflection may be betrayed. Though too much
+importance should not be attached to results of deflection
+tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each
+case, gives a good general idea of what may be expected in
+a fresh instance, any material departure from which should
+be a reason for specific inquiry as to the cause. A further
+reason with new work is found in the evidence it affords as
+to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case
+of floor beams, in what way the load is distributed amongst
+them, if, indeed, there be any such distribution.</p>
+
+<p>The author has commonly found that new work gives
+greater deflections than old&mdash;i.e., while calculation gives
+the same result for each, it does not apply equally well to
+both. The differences may be accidental, but are probably<span class="pagenum"><a name="Page_86" id="Page_86">[86]</a></span>
+due to other causes, perhaps to the fact that new work has
+not by repeated applications of load lost the resilience of
+parts liable to considerable local stress, such as is very liable
+to occur at connections, so that the deflection is, whilst new,
+greater than after many years&#8217; use, by which time such parts
+may develop a definite &#8220;set,&#8221; and contribute in a less degree,
+or not at all, to the total elastic deformation.</p>
+
+<p>It is also possible, as already suggested, that repeated
+high stress may reduce the ratio of strain to stress, the
+material gradually becoming more rigid, the modulus of
+elasticity being, in fact, increased.</p>
+
+<p>In girders of ordinary construction, the major part of
+the deflection is due to the booms, the remainder to the web;
+the latter is for plate girders a small amount only, and is
+commonly neglected, but for open web constructions it may
+be quite appreciable. For any given type of web arrangement
+the deflection due to the web will, for all depths, remain
+a constant quantity for the same span and unit stress; and
+though a moderate fraction of the whole deflection for a
+shallow girder, it may be a very considerable part for a girder
+of great depth, in which that part due to the booms is, of
+course, smaller, since the deflection due to these varies
+inversely as the girders&#8217; depths.</p>
+
+<p>Deflection, being dependent upon the elasticity of the
+material, is of necessity very largely influenced by the value
+of its modulus E, itself liable to considerable variation, and
+is increased in a small degree by the yield of joints and rivets,
+which effect, apart from the initial &#8220;set&#8221; of the girders,
+appears to be negligible. The stiffness of members in resisting
+angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less,
+and, finally, section excess at joints and gusset attachments
+has an influence in modifying deflection as compared with
+that due to the normal gross sections simply.</p>
+
+<p><span class="pagenum"><a name="Page_87" id="Page_87">[87]</a></span></p>
+
+<p>From these considerations it is apparent that any simple
+deflection formula must be largely empiric in its nature.
+For plate girders of uniform depth and flange stress, the
+writer has found the following to give good results<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D &times; C</span></span> &times; <i>f</i> = deflection in inches.</p>
+
+<p>The span S and depth D are, as a matter of convenience,
+taken in feet; the constant C is for wrought iron 3500, and
+for mild steel 4000; <i>f</i> is the mean of the extreme tensile
+and compressive stresses of the booms, in tons per square
+inch, estimated upon the gross sections.</p>
+
+<p>This, though satisfactory for plate girders, is not so suited
+to girders having open webs, in which the deflection will
+more nearly be</p>
+
+<p class="formula"><span class="fsize150">(</span><span class="division"><span class="num">3S</span><span class="denom">C</span></span> + <span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D &times; C</span></span><span class="fsize150">)</span> &times; <i>f</i>,</p>
+
+<p>the constant C being 3900 and 4450 for iron and steel respectively.
+The latter values of C correspond to normal
+values of the modulus of elasticity of 11,700 and 13,350 tons
+for iron and for steel, it being assumed that any slight rivet
+yield is off-set by any small section excess&mdash;say, 5 per cent.;
+it may, however, happen that section excess is greater than
+assumed, in which case some allowance may properly be made
+for this by increasing C.</p>
+
+<p>To adapt the formul&aelig; to girders other than those having
+parallel booms and uniform stress, the results, as deduced
+above, may be multiplied by constants given in column B of
+the Table given on <a href="#Page_93">page 93</a>.</p>
+
+<p>The practice of adopting for E in deflection formul&aelig; a
+quantity much smaller than its nominal amount, with the
+object of allowing in riveted girder work for the yield of
+rivets and of joints, can hardly now be defended, whatever
+may have been a case at a time when workmanship was much<span class="pagenum"><a name="Page_88" id="Page_88">[88]</a></span>
+inferior, when there was no machine riveting, and joints
+were, owing to the small weight of plates and bars, three
+times as numerous.</p>
+
+<p>The initial &#8220;set&#8221; of a girder consequent upon first loading
+is a quantity quite distinct from deflection proper, and may
+be so small as to be negligible, or read 10 per cent. of the
+true deflection, varying with design and workmanship.</p>
+
+<p>No estimate of girder deflection can be even approximately
+true if there is, at the level of the top or bottom flanges, a
+plated or otherwise rigid floor system which is not taken into
+account, as this will have the effect of very materially reducing
+the boom stress. To neglect this influence, where it
+exists, must necessarily lead to disappointing results, and it
+is quite practicable in many instances to include it in the
+calculation.</p>
+
+<p>The influence of angular distortion between the various
+members has been neglected. It may be pointed out, however,
+that the resistance accompanying these movements in
+girders having riveted connections, though unimportant as
+affecting deflection, is worth some consideration in regard
+to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount
+for any span, but will generally be of less importance in large
+girders than in small, because in large girders the ratio of the
+breadth of members to their length is commonly less.</p>
+
+<p>When determining the probable deflection of any girder
+of exceptional figure, it will be found convenient to make a
+strain diagram&mdash;an old device, in which the actual alterations
+of length being ascertained for all members, the girder is
+carefully set out to a suitable scale, with the lengths of
+members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the
+probable deflection. The value of E for this purpose should
+never be taken at less than the normal amount, and may for<span class="pagenum"><a name="Page_89" id="Page_89">[89]</a></span>
+a considerable excess of metal in joints and gussets be made
+as much as 10 per cent. greater, this being a convenient
+means of making the necessary correction.</p>
+
+<p>The effect of loads quickly applied may here be considered
+in connection with elastic deformations of girders
+of the same span, but different depths. If these be designed
+for similar loads and unit stresses, the deflections due to
+webs and booms of the girders compared will bear the same
+relation, each to each, as do the weights, whether in both
+cases the loads be inert or quickly applied, from which it
+follows that the mechanical &#8220;work&#8221; done by the loads in
+falling through the deflection heights is, neglecting inertia,
+always in proportion to the girderwork weights, and is a
+similar amount per ton, which as the total length of members
+remains substantially unaltered, corresponds to a similar
+amount of work per unit of section, or similar stress, irrespective
+of the depth of the girders.</p>
+
+<p>But for a &#8220;drop&#8221; load, as when there is some obstruction
+upon a railway bridge, there will be in addition a further
+amount of work to be absorbed, which is to be considered
+the same whatever the girder&#8217;s depth, and will for deep
+girders be a larger amount per ton of girderwork than in
+those that are shallow; this, taking effect on members of
+the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in
+the booms.</p>
+
+<p>The influence of the girder&#8217;s inertia in modifying drop-load
+effects will also be less marked in deep&mdash;i.e., light&mdash;girders
+than in girders shallow and heavy.</p>
+
+<p>It is, notwithstanding all this, desirable that the depth
+of main girders should be liberal for economy&#8217;s sake, and
+also that of floor beams, for reasons already dealt with; the
+probability of the drop load is somewhat remote, and, though
+possible, would simply induce, if it occurred, an increment<span class="pagenum"><a name="Page_90" id="Page_90">[90]</a></span>
+of stress rather more important in deep girders, making it
+specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact
+effects.</p>
+
+<p>It should be remarked that for short and very flexible
+beams, generally outside the limits of practice, there may
+also be, under quickly moving loads, a material increase of
+stress due to the centrifugal effort of the load on running
+round the deflection curve, and in rising upon the steep part
+of the curve beyond the girder&#8217;s centre. Where advisable,
+these effects may be modified by cambering the rail.</p>
+
+<p>For pin bridges in which there may be spring in the
+pins, excess stress in some eye-bars due to inequalities of
+length, and a want of that rigidity peculiar to riveted structures,
+the deflection will be greater than above indicated for
+girders of the ordinary English type.</p>
+
+<p>The method in common use for measuring the deflections
+of girders but a moderate distance above the ground
+by means of sliding-rods, though crude, gives, with care,
+results sufficiently accurate for most practical purposes; but
+some points necessary to remember may be mentioned with
+propriety. The lower rod should rest firmly upon something
+solid, say a stone, well bedded and free from any tendency
+to rock; the upper end should bear against some part of
+the girder above, presenting a hard surface, free from dirt
+or scale, and as the running load approaches the bridge it
+should be ascertained that there is no slack, that the rods
+bear hard at the top and bottom. The upper end having
+been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other.
+These precautions are so self-evident that an apology is
+almost necessary for mentioning them.</p>
+
+<p>To ascertain deflections with a single pair of rods is only
+allowable when the girders rest firmly on their bearings; if<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span>
+felt has been placed under the girder ends, or if the bedstones
+are insecure or rocking, it is necessary to use three
+pairs of rods, one pair at the middle and a pair at each end,
+in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the
+desired result.</p>
+
+<p>In the case of a number of spans in series, each resting
+upon sill girders common to two sets of bearings, this
+method also gives results of indifferent reliability, as the
+depression of each end may be greater as the travelling load
+comes upon and leaves the span than when it is precisely
+over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular
+position of the running load, which are what is required.</p>
+
+<p>The author suggests, as a means of ascertaining deflections
+free from these objections, that it should be done by
+first measuring the slope at one end, and from this deducing
+the deflection at the centre.</p>
+
+<p>This is to be accomplished by means of a little instrument,
+consisting of a telescope with cross-hair sights, and
+fitted with a reflecting prism at the eye-piece capable of
+being turned round, so that the observer has a wide choice
+as to the position he assumes with reference to the instrument,
+and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one
+end of the girder over the bearing, at the other end a scale
+is secured, to which the telescope is directed, the cross hair
+being made to sight on the zero of the scale, or the reading
+noted. For a girder supposed to deflect to uniform curvature
+(say, with uniform depth and uniform stress, the
+ordinary case) the reading observed will be four times the
+deflection; every <sup>1</sup>&#8260;<sub>10</sub> inch actual reading on the scale will
+correspond to <sup>1</sup>&#8260;<sub>40</sub> inch of girder deflection.</p>
+
+<p>Apart from the deflection, this method gives a ready<span class="pagenum"><a name="Page_92" id="Page_92">[92]</a></span>
+means of observing the end slope, a quantity of equal value
+for purposes of comparison. As with girders of similar proportions,
+and similarly stressed, the deflection will at all
+spans be the same fraction of the span; so should the end
+slope be a constant quantity under similar conditions, the
+diagram, <a href="#Fig54">Fig. 54</a>, will make the principle quite clear.</p>
+
+<div class="figcenter"><a name="Fig54" id="Fig54"></a><a name="Fig55" id="Fig55"></a><a name="Fig56" id="Fig56"></a><a name="Fig57" id="Fig57"></a>
+<img src="images/illo104.png" alt="" width="350" height="429" />
+<p class="caption"><span class="smcap">Figs.</span> 54 to 57.</p>
+</div>
+
+<p>Strictly the character of the deflection curve is slightly
+modified by that part of the deflection due to the web; so
+that the depression at the centre would, in the case assumed
+above, be somewhat more than one-fourth part of the end
+reading, and generally will be a larger fraction of the reading
+than that deduced from a consideration of flange stress<span class="pagenum"><a name="Page_93" id="Page_93">[93]</a></span>
+simply. In <a href="#Fig55">Figs. 55 to 57</a>, which are intended to explain
+this, it will be noticed that deflection due to the web is
+shown straight-lined from the bearings to the centre of the
+girder; this is strictly true only for a girder correctly designed
+for an immovable distributed load; but as there
+should be for girders intended for a travelling load, some
+excess in web members near the centre under the condition
+of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as
+shown in the diagram for the sake of simplicity.</p>
+
+<p>Suitable constants, including the corrections necessary,
+are given in column A of the table annexed for a few typical
+cases, and by these constants the actual readings should be
+multiplied to find the deflection. The constants have been
+worked out for depths of one-tenth the span; for greater
+depths they should be slightly more, and for smaller depths
+somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly
+exceeding 5 per cent., and generally much less.</p>
+
+<p>The figures in column B relate to the formul&aelig; previously
+stated, and apply equally well to all depths.</p>
+
+<p class="center"><span class="smcap">Tables of Multipliers for Deflection.</span></p>
+
+<table summary="Table page 93">
+
+<tr>
+<td class="left padr3"><i>Uniform Stress</i>:</td>
+<td class="center padl1 padr1">A.</td>
+<td class="center padl1 padr1">B.</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3">Girders of uniform depth, varying flange section</td>
+<td class="center bot padl1 padr1">0&middot;27</td>
+<td class="center bot padl1 padr1">1&middot;00</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3">Hog-backed girders, ends half of centre depth, varying flange section</td>
+<td class="center bot padl1 padr1">0&middot;24</td>
+<td class="center bot padl1 padr1">1&middot;08</td>
+</tr>
+
+<tr>
+<td colspan="3" class="left padr3"><i>Varying Stress</i>:</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">[A]</a>Girders of uniform depth and flange section</td>
+<td class="center bot padl1 padr1">0&middot;32</td>
+<td class="center bot padl1 padr1">0&middot;87</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Hog-backed girders (as above), but uniform flange section</td>
+<td class="center bot padl1 padr1">0&middot;29</td>
+<td class="center bot padl1 padr1">0&middot;97</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Bow-string girders of uniform flange section</td>
+<td class="center bot padl1 padr1">0&middot;16</td>
+<td class="center bot padl1 padr1">1&middot;30</td>
+</tr>
+
+</table>
+
+<div class="footnote">
+
+<p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">[A]</span></a> For uniform loading.</p></div>
+
+<p><span class="pagenum"><a name="Page_94" id="Page_94">[94]</a></span></p>
+
+<p>It is apparent that, if preferred, the scale, instead of
+being in inches, divided suitably, may, for each type of
+girder, be amplified to the proper degree, so that the amount
+of the deflection may be read off at once.</p>
+
+<p>This method of dealing with deflections is quite independent
+of the character of the bearings, and is applicable
+to girders at any height above ground or over water; but
+its use would hardly be practicable for very small beams, or
+those in an awkward position, or near which it would be
+impossible to remain with a running load upon the bridge.</p>
+
+<p>There is a possible source of error in the use of the
+instrument, most likely to occur with triangulated girders,
+with which, if the instrument is placed at the top of an end
+post, the reading observed may be the joint effect of deflection
+and of local flexure of the members meeting near the
+telescope. This may be tested, and, if necessary, allowed
+for, by first sighting upon a scale at the next apex, and
+observing the effect of the moving load. Again, as girders
+sometimes cant towards the running load, if the instrument
+is placed on one edge of a girder, and the cantings of the
+two ends are dissimilar, a false reading will result, which
+may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between
+the cants upon the observation. Only in exceptional cases
+is it likely that either of these considerations would need
+attention.</p>
+
+<p>The author has secured with this instrument very promising
+results, notwithstanding that under a running load there
+is a slight haziness of the scale as seen through the telescope,
+due to &#8220;dither,&#8221; largely the result of imperfections which
+may be remedied.</p>
+
+<p>Deflections may sometimes be conveniently taken, by a
+quick-eyed observer, with a good surveyor&#8217;s level and a
+specially-divided staff held at the centre of the girder. The
+divisions preferred by the author for this purpose are <sup>1</sup>&#8260;<sub>10</sub> inch,<span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span>
+plainly marked, which may be seen at 50 feet distance with
+sufficient clearness to make possible readings by estimation
+between the divisions to, say, <sup>1</sup>&#8260;<sub>50</sub> inch. But it is clearly
+desirable not to rely upon a single observation only, where
+all the evidence is gone so soon as the sight has been taken.</p>
+
+<p>In rail-bearers, or other short girders, it may not be
+practicable to adopt such methods, either on account of an
+inability to find a suitable place for the instrument, or to
+read with any telescope with sufficient promptitude as the
+load passes rapidly over. The use of rods may also be out
+of the question, as the errors attending their manipulation
+may be serious where but a small movement has to be noted,
+this being complicated in some instances by the bearings
+being insecure, and working to an extent which obscures the
+measurement sought. In such cases it is preferable to use
+a stiff slat lying along the girder, which bears, through
+short blocks over the girder bearings, upon the flanges; the
+deflection is then read by direct measurement of the girder&#8217;s
+depression at the centre, relative to the slat.</p>
+
+<p>The author is, unfortunately, not able to give any precise
+information on the effect of running-load as against a
+load that is stationary in connection with girder deflections.
+It is by no means easy in ordinary work upon a railway to
+secure facilities for making such comparative tests. It may,
+however, be confidently stated, as a result of such observations
+as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a
+50 feet span, but little greater than that due to the same
+load stationary; it may be, perhaps, 5 to 10 per cent. more.</p>
+
+<p>It is evident that to determine the precise difference
+where the quantity to be measured is so small needs apparatus
+of a more delicate character than that in common use,
+and the control of an engine, or engines, for the purpose of
+making the special tests, conditions which on a busy line can
+only be secured by special arrangements previously made.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_96" id="Page_96">[96]</a></span></p>
+
+<h2>CHAPTER IX.<br />
+<span class="chaptitle">DECAY AND PAINTING.</span></h2>
+
+<p>The author has collected particulars as to the amount and
+rate of rusting in metallic structures which are of some
+interest. In all such instances it is very necessary to note
+the conditions which have obtained during the process of
+wasting, as without this, misleading conclusions may be
+drawn. The information given relates in all cases to wrought
+iron, unless otherwise stated.</p>
+
+<p>A plate-girder bridge, having girders under rails, was
+found to be badly rusted. The atmospheric conditions were
+unusually trying, the air being damp and impregnated with
+acid fumes from adjacent steel works. That the wasting
+was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than
+those farther removed and partly sheltered from the corrosive
+influence.</p>
+
+<p>The webs were in places eaten right through, having
+lost a mean amount of about <sup>1</sup>&#8260;<sub>8</sub> inch full on each surface in
+twenty-eight years. Painting had not been well attended to.</p>
+
+<p>In a similar bridge, not a great distance from this, but
+sufficiently far away to modify the conditions for the better,
+considerable wasting was also observed, but more particularly
+where the girders had been built into masonry, which,
+loosening with the constant movement of the girder-ends,
+had allowed moisture to collect, and rust to develop, without
+the chance of repainting these surfaces. The amount of
+waste at the places indicated was, as in the last case, about<span class="pagenum"><a name="Page_97" id="Page_97">[97]</a></span>
+<sup>1</sup>&#8260;<sub>8</sub> inch on each face, and in the same time, other parts of
+the girders having suffered less.</p>
+
+<div class="figcenter"><a name="Fig58" id="Fig58"></a>
+<img src="images/illo109.png" alt="" width="350" height="60" />
+<p class="caption"><span class="smcap">Fig.</span> 58.</p>
+</div>
+
+<p>A third plate-girder bridge, with outer main girders,
+cross-girders, and plated floor, carrying a road over a railway
+and sidings, and which was known to have been
+neglected in the matter of painting, was very badly rusted,
+both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration
+was, however, the smoke and steam from locomotives, which
+frequently stood for some time, during shunting operations,
+directly under the bridge. The webs of the cross-girders,
+which were originally <sup>1</sup>&#8260;<sub>4</sub> inch thick, had rusted into occasional
+holes during fourteen years&mdash;i.e. <sup>1</sup>&#8260;<sub>8</sub> inch from each
+surface in that time. When removed a little later the
+wasting was so complete that it was possible to knock out
+with a light hammer the remains of the web between flanges
+and stiffeners, so as to leave an open frame only. One of
+the cross-girders was so treated by the men engaged upon
+the work, when it presented the appearance shown in <a href="#Fig58">Fig. 58</a>.</p>
+
+<p>In another case&mdash;that of a bridge with lattice girders
+under rails&mdash;the ends were built into masonry, which had,
+of course, loosened, with the usual result. The air of the
+locality was certainly pure, but somewhat damp. The general
+condition of the ironwork was good, but end-bars of the
+diagonal bracing, where they had been closed in, had lost
+<sup>1</sup>&#8260;<sub>8</sub> inch on each surface in thirty-three years. The top flanges
+immediately under the timber floor were in a very fair state,
+which is of some interest when it is considered that these<span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span>
+were made of steel of the same kind as that already noticed
+as being used in the construction of small girders (see <a href="#Fig46">Fig.
+46</a>, <i>ante</i>), described in the chapter upon &#8220;<a href="#Page_61">High Stress</a>,&#8221; both
+cases dating from the year 1861. The painting upon the
+lattice-girder bridge had been pretty well attended to; but
+in the case of the small steel girders it had been greatly&mdash;perhaps
+altogether&mdash;neglected; this, coupled with adverse
+atmospheric conditions, had produced the result that the
+rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully
+<sup>1</sup>&#8260;<sub>8</sub> inch on each surface, as against a negligible amount
+under the more favourable circumstances.</p>
+
+<p>Girder-work over sea-water, as in piers, seems to rust at
+a sensibly greater rate than inland work under average conditions;
+but it is hardly practicable to make any strict
+comparison, as in either case the rate of oxidation is so
+much affected&mdash;even controlled&mdash;by the care bestowed upon
+the structures. This general conclusion is based upon the
+results of examination of wrought-iron girder-work over sea-water
+of ages varying from fourteen to forty-four years. It
+should be remarked, however, that in one case steel girders
+but five years old, and which were frequently wetted with
+sea-spray, were found to be wasting rather badly&mdash;the paint
+refusing to keep upon the surface.</p>
+
+<p>It may be concluded from the above instances, and from
+others which have come under notice, that wrought-iron
+work, if not properly cared for in respect to painting, or
+under conditions otherwise bad, may be expected to rust at
+a rate which corresponds to the loss of <sup>1</sup>&#8260;<sub>8</sub> inch on each surface
+in from fifteen to thirty years; but with proper care as
+to painting, and exclusive of exceptionally bad conditions,
+it does not appear to waste at any measurable rate. In some
+instances, upon scraping the paint from girders which had
+been in use for thirty years, the author has found, beneath the<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span>
+original red lead, the metallic surface bright and clean,
+showing no trace of rust.</p>
+
+<p>Of ordinary steelwork the same cannot be said, the common
+experience being that mild steel is very liable to be
+attacked by rust. With passable care in the bridge-yard
+during manufacture, such that with wrought iron no after-trouble
+would be noticeable, steel is very liable to show,
+within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away
+discloses a small rust-pit. This is more often seen on the
+flange surfaces (horizontal) than on web surfaces (vertical),
+but it is probable the position has little to do with the
+matter, and that it is rather due to the fact that rust has
+been earlier started on the flange-plates, upon being put
+through the drilling-machines and inundated with slurry,
+which occurs only to a more limited extent with webs having
+fewer holes. The heads of steel rivets do not show this
+tendency to &#8220;pit,&#8221; or to early development of rust. The
+riveting is about the last operation in making a girder, each
+rivet being freed of all rust by heating, and quickly coming
+under the protection of oil or paint. It may happen in this
+way that the heads of rivets on a girder may be exposed
+without protection for as many hours only as the rest of the
+work for weeks, which fully accounts for the difference in
+behaviour.</p>
+
+<p>The essential point to be observed in all steelwork is to
+prevent, if possible, the first development of rust, for once
+begun it is much more difficult to arrest than in iron; for
+this reason, oiling of all material for a steel bridge, at a very
+early stage of its existence, cannot be too strongly insisted
+upon. This practice, however, makes the work so objectionable,
+and even dangerous when being lifted&mdash;because of the
+liability to slip&mdash;to the men engaged upon it, that it is
+commonly very difficult to ensure it being done sufficiently<span class="pagenum"><a name="Page_100" id="Page_100">[100]</a></span>
+soon to satisfy a careful inspector. If the work is carried
+out under cover, the requirement is less urgent. Strictly,
+all material should be oiled so soon as rolled, but the author
+does not remember to have seen this done at any of the
+mills he has visited, though it is common enough to find it
+specified.</p>
+
+<p>Ironwork does not need the extreme care which should
+be bestowed upon steelwork, but it is desirable that it should
+be painted as soon as possible, the surfaces being first
+thoroughly cleaned.</p>
+
+<p>There is, probably, for painting girder work nothing to
+beat good red lead as a protective coating; but there is considerable
+difficulty in getting it reasonably pure, without
+which quality its utility will be greatly reduced. The question
+of purity will, however, be found to be largely a question
+of price. It may be stated broadly that, whether for steel
+or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.</p>
+
+<p>In repainting old work, care should be taken to remove
+all traces of rust previous to laying on the new coat. It is
+not an altogether uncommon practice to repaint old structures
+by dealing only with the parts readily accessible, which,
+being less liable to rust, probably but little need it; leaving
+those parts which are difficult of access, and where rust is
+developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said,
+is indefensible. It is better rather to neglect the surfaces
+freely exposed and ventilated, and devote the whole care
+upon those other parts, confined and difficult to get at;
+taking the trouble necessary to remove ballast, timber, or
+whatever may obstruct the operation, in order that the bad
+places may be thoroughly scraped, and then painted. Those
+parts which most need attention may cost, perhaps, to reach&mdash;and
+deal with when exposed&mdash;ten times as much per yard<span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span>
+of surface as the rest of the superfices, which needs little,
+and is always accessible; but the cost should not deter the
+proper carrying out of the work, as it will prove the very
+worst sort of economy to deal with painting in a perfunctory
+manner.</p>
+
+<p>It should be noted that girder work, whether of wrought
+or cast iron, when embedded in lime or cement concrete, or
+mortar, generally proves to be very well preserved, provided
+that close contact has obtained. Cast-iron girders, when
+carrying jack arches resting upon the bottom flanges, are
+found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of
+new girders. Much the same remarks apply to girders of
+wrought iron carrying jack arches, where protected by the
+brickwork; provided that the girders are sufficiently stiff to
+minimise deflection, and allow the masonry or brickwork to
+adhere to the surfaces.</p>
+
+<p>Such girders are in a very different condition to those
+previously referred to, in which the ends of the girders,
+carrying a light floor structure, are built into masonry where
+the deflection slope is greatest; though, apart from the few
+cases where adherence can be relied upon, building-in is an
+undesirable practice, and has the disadvantage that after-examination
+is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted
+to.</p>
+
+<p>Cast iron has ordinarily&mdash;unlike wrought iron or steel&mdash;great
+capacity for resisting rust, and will, after many years
+of absolute neglect, appear but little the worse; an advantage
+which is the more pronounced when considered relatively
+to the greater thickness of the thinnest parts in
+cast-iron girders, the percentage of waste being proportionately
+lessened.</p>
+
+<p>Cast iron does, however, behave somewhat badly in sea-water,<span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span>
+the metal sometimes losing its original character, and
+becoming in time quite soft; though, if not worn away, as
+by the attrition of shingle, maintaining its original bulk.</p>
+
+<p>Of some forty-five cast-iron piles belonging to various
+structures, examined whilst engaged upon sea-pier work for
+Mr. St. George-Moore, though the author found somewhat
+diverse results, in no case did there appear to be any general
+softening of the whole thickness, but a distinct change for
+some definite distance inwards, generally to be decided without
+difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of
+softening was found close to the ground, this depth rapidly
+decreasing higher up, till, at a height of 5 feet, but little if
+any softening could be detected. At 2 feet above ground
+the softening was frequently but one-quarter of that at
+ground level. There was, too, often a considerable difference
+in the behaviour of different piles in the same structure
+under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly
+none at all. For six different structures the amount of
+softening near ground level, of about twenty-five piles
+examined, was as given in the table on the next page.</p>
+
+<p>The greatest depth of softening found (see No. 2) was
+<sup>9</sup>&#8260;<sub>16</sub> inch, 1 foot above ground, in a pile thirty-six years old.
+The decayed material when removed was of a soft, greasy
+consistency, perfectly black, which a few hours later was
+found to have changed to a dry yellow powder, by the rapid
+absorption, it may be supposed, of atmospheric oxygen. It
+is apparent, therefore, from this example that deterioration
+may proceed to a considerable depth; but it should be
+observed that other piles of the set showed softening at
+ground level of <sup>1</sup>&#8260;<sub>8</sub> inch only.</p>
+
+<p class="center"><span class="smcap">Softening of Cast-Iron Piles in Sea-Water.</span><span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span></p>
+
+<table class="nowrap" summary="Table page 103">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">No.</th>
+<th colspan="2" class="center padl1 padr1 br">Age.</th>
+<th colspan="2" class="center padl1 padr1 br">Maximum<br />Softening.</th>
+<th colspan="6" class="center padl1 padr1 br">Maximum<br />Rate of<br />Softening.</th>
+<th colspan="5" class="center padl1 padr1 br">Mean Rate<br />of<br />Softening.</th>
+<th class="center padl1 padr1 br">Quality<br />of<br />Metal.</th>
+<th class="center padl1 padr1 wrappable">Materials Entered<br />by Piles.</th>
+</tr>
+
+<tr>
+<td class="center top br">1</td>
+<td class="right top padl1">17</td>
+<td class="center top padr1 br">years</td>
+<td class="center top"><sup>5</sup>&#8260;<sub>16</sub></td>
+<td class="center top br">in.</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top padr0">7</td>
+<td>&nbsp;</td>
+<td class="center top padr1 br">years</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top">15</td>
+<td class="center top br">years</td>
+<td class="center top br">Soft</td>
+<td class="left top padl1 padr1 wrappable">Extremely soft sandstone.</td>
+</tr>
+
+<tr>
+<td class="center top br">2</td>
+<td class="right top">36</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>9</sup>&#8260;<sub>16</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">8</td>
+<td class="left top padl0"><sup>1</sup>&#8260;<sub>2</sub></td>
+<td class="center top br">&#8222;</td>
+<td colspan="5" class="center top br">No result</td>
+<td class="center top br">&#8222;</td>
+<td class="left top padl1 padr1 wrappable">Rubble mound.</td>
+</tr>
+
+<tr>
+<td class="center top br">3</td>
+<td class="right top">32</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>3</sup>&#8260;<sub>8</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">11</td>
+<td>&nbsp;</td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top">15</td>
+<td class="center top br">years</td>
+<td class="center top padl1 padr1 br wrappable">Moderately hard</td>
+<td class="left top padl1 padr1 wrappable">Fine sand.</td>
+</tr>
+
+<tr>
+<td class="center top br">4</td>
+<td class="right top">38</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>1</sup>&#8260;<sub>10</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">47</td>
+<td>&nbsp;</td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top">140</td>
+<td class="center top br">&#8222;</td>
+<td class="center top br">Hard</td>
+<td class="left top padl1 padr1 wrappable">Extremely hard rock.</td>
+</tr>
+
+<tr>
+<td class="center top br">5</td>
+<td class="right top">17</td>
+<td class="center top br">&#8222;</td>
+<td colspan="2" class="center top br">Small</td>
+<td colspan="6" class="center top padl1 padr1 br">Negligible</td>
+<td colspan="5" class="br">&nbsp;</td>
+<td class="center top br">(?)</td>
+<td class="left top padl1 padr1 wrappable">Sand and Shingle.</td>
+</tr>
+
+<tr class="bb">
+<td class="center top br">6</td>
+<td class="right top">14</td>
+<td class="center top br">&#8222;</td>
+<td colspan="2" class="center top padl1 padr1 br">Negligible</td>
+<td colspan="6" class="center top br">Ditto</td>
+<td colspan="5" class="br">&nbsp;</td>
+<td class="center top br">(?)</td>
+<td class="left top padl1 padr1 wrappable">Sand.</td>
+</tr>
+
+</table>
+
+<p>The least rate of softening noticed, apart from those
+structures of a more recent date, in two of which it was<span class="pagenum"><a name="Page_104" id="Page_104">[104]</a></span>
+very slight, occurred in a pier thirty-eight years old (No. 4),
+where, of three piles tested, two were quite hard, and the
+third softened <sup>1</sup>&#8260;<sub>10</sub> inch only.</p>
+
+<p>Whatever may be the precise cause of the change, it
+does not appear to be affected by the period or percentage
+of immersion during the rise and fall of tides.</p>
+
+<div class="figcenter"><a name="Fig59" id="Fig59"></a>
+<img src="images/illo116.png" alt="" width="500" height="397" />
+<p class="caption"><span class="smcap">Fig.</span> 59.</p>
+</div>
+
+<p>This will be clear from the diagram, <a href="#Fig59">Fig. 59</a>, which
+refers to four piles (No. 3 of table), all of the same age, in
+the same structure. On each pile the depth of softening is
+given at points in strict relation to each other, and to the
+tidal range. The percentages of immersion for the various
+heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening;
+this, indeed, is always greatest near the ground, at
+whatever actual height it may be. For instance, pile A was<span class="pagenum"><a name="Page_105" id="Page_105">[105]</a></span>
+at ground-level softened <sup>1</sup>&#8260;<sub>4</sub> inch, that point being 60 per
+cent. of its life under water; but on pile B, at a point 74
+per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level
+of this pile, the percentage being there 87, the softening
+was no greater than at ground-level at pile A.</p>
+
+<p>It is probable that while the percentage of submersion
+in moving water hardly appears to affect the result, yet prolonged
+contact with wet sand, sea-weed, or clinging shell-fish
+may do so. This seems to suggest that the process of change,
+as between the sea-water and the iron, is slow, and to be
+effective must be continuous; so that it is only found to
+any considerable extent where the water in contact with the
+surface is still. In the two worst cases, Nos. 1 and 2 of the
+table, at points 1 foot and 6 inches above ground-level,
+the surface was in one pile shrouded in a thick mantle of
+heavy sea-weed, and in the other covered by molluscs; in
+both instances the surfaces being thus kept moist and undisturbed.
+The piles of the fourth case were in hard rock,
+were clean, and, where accessible, always either in moving
+water or quite dry.</p>
+
+<p>However this may be, the power to resist softening
+certainly appears to vary largely with the quality of the
+iron. The piles, referred to above, in which deterioration
+proceeded at the most rapid rate were certainly of a soft
+metal, the first being markedly so. On the other hand,
+certain piles (No. 4) of hard, close-grained iron suffered very
+little.</p>
+
+<p>It may be mentioned with respect to the last named, as
+a matter of interest, that the caps of the lower lengths (just
+above ground-level) had been cast with short pieces of
+wrought iron projecting&mdash;possibly for lifting purposes&mdash;which
+during thirty-eight years had altered in character to
+something very like softened cast iron, but laminated, and<span class="pagenum"><a name="Page_106" id="Page_106">[106]</a></span>
+harder. Of about 1<sup>1</sup>&#8260;<sub>4</sub> inch original thickness, only <sup>3</sup>&#8260;<sub>16</sub> inch
+remained having the semblance of wrought iron. The
+percentage of submersion was about 60.</p>
+
+<p>A number of piles, not included in the table, varying
+from fifteen to forty-four years old, and of the same structure
+to which set No. 2 belonged, were all found to be hard,
+with the exception of one showing <sup>3</sup>&#8260;<sub>16</sub> inch of softening.
+These are omitted, because the mud surrounding them was
+at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points
+testing might have disclosed different results. It is probable
+that for any piles standing in soft material examination
+below the surface would reveal more pronounced softening
+than where occasionally exposed.</p>
+
+<p>To meet the effects of sea-water on cast-iron piles, and
+for other reasons, it is a common and good practice to make
+the lower lengths of greater thickness&mdash;say, <sup>3</sup>&#8260;<sub>8</sub> inch more&mdash;than
+that sufficient for the upper. Occasionally, also, the
+bottom lengths are filled with concrete, which no doubt adds
+to the length of time during which they may be relied upon.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span></p>
+
+<h2>CHAPTER X.<br />
+<span class="chaptitle">EXAMINATION, REPAIR, AND STRENGTHENING OF
+RIVETED BRIDGES.</span></h2>
+
+<p>In the preceding chapters defects of various kinds to which
+riveted bridgework is liable have been more particularly
+dealt with; it is now proposed to consider the examination
+of such structures, following this by a reference to methods
+of repair and strengthening, leaving the treatment of other
+classes of bridgework to be developed under their proper
+headings, though some of the remarks immediately following
+will apply to all.</p>
+
+<p>The exhaustive survey of a bridge is only to be made
+after considerable experience in the work, but it may be
+stated that in looking for defects it is well to seek where they
+are least expected, till, with practice, one knows better where
+to direct attention. When examining with a view to pronouncing
+an opinion upon the fitness of the structure to
+remain in place, if in any real doubt, it is wise to give a
+casting vote against it; and finally it may be said that upon
+taking down a bridge condemned for any one or more defects,
+it should be examined for worse. This may seem to be
+somewhat pessimistic, but is based upon the teachings of
+experience.</p>
+
+<p>Preliminary examination of a bridge may reveal such
+faults or weaknesses as at once to ensure its condemnation;
+but if this is not the case, and there is a reasonable probability
+that the structure may be given a fresh lease of life,
+it will, for the purpose of estimating the strength, or for<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span>
+possible repairs, commonly be desirable to secure precise
+particulars of the existing structure independently of any
+drawings that may be in existence, and which will very
+probably be incorrect, the finished work, if old, seldom
+agreeing with the contract drawings. A final decision may in
+this case be deferred till after the measuring up has been
+completed, the condition of the structure becoming more
+familiar in the process.</p>
+
+<p>It is desirable first to ascertain whether the bridge
+remains in good form, whether the camber of girders appears
+to be what might be expected, or agreeable with existing
+records, though much reliance must not be placed upon
+figured cambers, it being quite common for girders to leave
+the bridge yards with the camber something other than
+that intended. The deflections under live load will also be
+observed, and compared with the calculated result, or checked
+by judgment. The calculations upon which strength and
+deflections are based will, of course, refer to the actual
+sections, which are sometimes a little difficult to ascertain if
+there has been irregular rusting. In continuous girders also,
+levels having been taken, allowance should be made for
+effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the
+like object. It is seldom that the main flanges of girders
+show signs of weakness, unless from flexure in the case of
+long and narrow top members, insufficiently stiffened; but
+there may be want of truth from other causes already dealt
+with. In plate girders the webs should be most carefully
+scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange
+angles, if the floor rest upon the flange. All riveted connections,
+of course, need close attention, both for straining
+effects, where there is a liability to wracking, and to detect
+loose rivets. Loose rivets and want of tightness in other<span class="pagenum"><a name="Page_109" id="Page_109">[109]</a></span>
+parts of the work may frequently be detected at sight by a
+reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects
+of weather; it may be seen round rivet-heads or along the
+edges of angle-bars, or other parts where there is movement.
+Loose rivets, though generally to be detected also by the
+hammer, may perhaps in the case of thin-webbed cross-girders
+be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may
+sometimes be detected by simultaneous deflection tests&mdash;with
+rods&mdash;at the top and bottom flanges of a girder, at the same
+distance from the bearings. Any difference in the readings
+may indicate loose web-rivets, or possibly a tear in the web
+running parallel to the flange angles.</p>
+
+<p>Bracings between girders are very apt to display a rich
+harvest of working rivets. Cross-girders and longitudinals
+also may have loose rivets at their connections, and be very
+badly wasted, with quite possibly cracks in the webs, or
+other defects already enlarged upon.</p>
+
+<p>The condition of the road upon the bridge will frequently
+be an indication of the state of the floor which carries it; or
+the existence of rail-joints which are working badly may
+very properly lead to a critical examination of the girder-work
+immediately below, as this is a fruitful source of
+damage in light constructions. Floor-plates, where these
+exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the
+latter being often loose and unsatisfactory.</p>
+
+<p>Trough floors may be expected to show loose rivets near
+the ends, with a probability of excessive leakage where they
+abut against the webs of supporting girders.</p>
+
+<p>Floor plates resting upon abutments or piers, being very
+liable to serious decay, require attention, and girder-work
+entering masonry should receive close scrutiny, any obstruction<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span>
+to a sufficient examination being removed so far as is
+judged sufficient for the purpose. The structure should, of
+course, be closely watched during the passage of live load
+for any signs of abnormal movement, excessive vibration, or
+lurching.</p>
+
+<p>In addition to seeking for these various defects, or others
+which have been referred to in these pages at length, it
+will be well always to be alive to the possibility of faults
+to be seen for the first time, or of which the author has
+furnished no instance.</p>
+
+<p>Having formed a reliable opinion as to the state of the
+bridge, this, if satisfactory, may leave to be determined only
+the question of strength relative to the loads carried. It is
+apparent that stress limits suitable for a new structure,
+which has all its life before it, of purpose moderate to cover
+possible deteriorations, the growth of loads, and other adverse
+influences, may to avoid immediate reconstruction, reasonably
+be permitted of a higher value for a further term of
+years in the case of a structure which it is known has for a
+considerable period behaved well, and remains in good condition.
+What this higher value may be will be greatly
+influenced by the circumstances of each case, and, being
+largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the
+nominal unit stress in an old bridge may be a very considerable
+amount in excess of that allowed for new work,
+without, of necessity, showing any ill effects; and the author
+is of opinion that for old bridges in good condition it is
+quite prudent to allow an excess of 33 per cent. beyond that
+permissible for a new design. If the structure is too weak
+to satisfy this modified condition, it may be possible to
+bring it within the stress limit by a reduction of ballast or
+other removable dead weight. If this expedient does not
+promise to be satisfactory, or the bridge shows actual signs of<span class="pagenum"><a name="Page_111" id="Page_111">[111]</a></span>
+weakness, or palpable defects, it will be necessary to deal with
+the question of repair, strengthening, or reconstruction.</p>
+
+<p>The repair of built up bridgework resolves itself largely
+into a matter of replacing loose rivets by cutting these out,
+rhymering the holes, if desirable, and again riveting. It
+will often be sufficient to do this with no particular precautions
+as to bolting up temporarily; the rivets having been
+loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to
+remove all the rivets, bolting up securely as this is done, in
+order to make a tight job, taking out each bolt in turn as
+required, and again filling the holes; or it may be well in a
+bad case first to remove all loose rivets, substituting good
+bolts, in order that work which has gone out of shape owing
+to defective rivets may first be brought true.</p>
+
+<p>Cross-girder webs, cracked vertically or nearly so, are
+commonly repaired with splice-plates on either side; but in
+doing this it is undesirable to add plates of excessive thickness
+relative to the web&mdash;probably poor&mdash;as by an abrupt
+change of web section it appears not unlikely a fresh break
+may be favoured.</p>
+
+<div class="figc450"><a name="Fig60" id="Fig60"></a><a name="Fig61" id="Fig61"></a><a name="Fig62" id="Fig62"></a><a name="Fig63" id="Fig63"></a>
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 60.</span> <span class="right49"><span class="smcap">Fig.</span> 61.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 60. and <span class="smcap">Fig.</span> 61.</p>
+<img src="images/illo124.png" alt="" width="450" height="376" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 62.</span> <span class="right49"><span class="smcap">Fig.</span> 63.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 62. and <span class="smcap">Fig.</span> 63.</p>
+</div>
+
+<p>Replacing wasted flange-plates, or adding new plates to
+those which exist, is occasionally resorted to in the case of
+main girders, the flanges of which are sufficiently accessible,
+but the operation is difficult, takes some little time, and
+should only be attempted under the constant supervision of
+a thoroughly capable man. When done, if the girder has
+not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the
+new section, the old always taking more by the amount of
+the dead-load stress previously carried. The method which
+the author has seen applied to lattice girders of about
+80 feet span, having good angle-bars in the flanges, with a
+shallow vertical web for attachment of diagonals, consisted<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span>
+in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been
+removed. The new plate length having been prepared, was,
+on a Sunday, during a few hours&#8217; cessation of traffic, marked
+off, the temporary bolts being removed for the purpose, and
+then replaced. After the plate had been drilled, on a later
+Sunday, it was finally put into position, bolted up, and
+riveted at leisure; cover-plates make additional trouble, but
+are dealt with on the same principle. The method as shown
+in <a href="#Fig60">Fig. 60</a> is, however, barely practicable for so many plates.
+It is preferable, if it is proposed to add section, to do this
+with as little interference as possible with existing rivets of
+importance. This may be accomplished, if the existing
+plates are not too wasted at their edges, by riveting on new
+strips or angle-bars (see <a href="#Fig61">Figs. 61 to 63</a>). Occasionally the
+strength of a girder is increased by the addition to the top<span class="pagenum"><a name="Page_113" id="Page_113">[113]</a></span>
+or bottom boom of material in such a form as sensibly to
+increase the depth, and thus, while adding increased section
+to one boom, to reduce the stress in each, though to dissimilar
+amounts. By this device also the relief is effective
+only as regards the live-load stress; under dead load only
+the new material does no work, provided, of course, that
+no relief staging was used during the alterations. For
+girders carrying any considerable proportion of dead load the
+method is very inefficient, though for others, in which the
+live load is relatively large, the result should be more satisfactory.</p>
+
+<p>As this question of adding new section to old is of much
+importance in dealing with repairs and strengthening operations,
+a few general remarks upon the subject will be
+pertinent. The difficulty in such work commonly is to
+cause the new to render any considerable assistance to the
+old in those cases which occur in practice. If a bar be
+imagined under longitudinal stress varying between 0 and a
+maximum, then, if the area of the piece be increased at the
+time when it takes no stress, its capacity for resisting the
+maximum amount will be increased, and for added material
+of similar elasticity the unit stress proportionately reduced.
+If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any
+degree. To take a third case, of the maximum being twice
+the minimum load, it will be necessary, in order to lower the
+maximum unit stress by 25 per cent., to double the original
+section of the bar if, as supposed, the extra metal has been
+added to the piece when under the smaller load, so that the
+new section is only effective in assisting to carry the remainder
+of the load at such times as it may be imposed.
+The relationship stands thus<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><span class="division"><span class="num">Live load</span><span class="denom">Live + dead load</span></span> &times; <span class="division"><span class="num">New area</span><span class="denom">New + old area</span></span> = relief.</p>
+
+<p><span class="pagenum"><a name="Page_114" id="Page_114">[114]</a></span></p>
+
+<p>These statements will be true under the conditions named,
+within the elastic limit of the material; but some advantage
+would be derived in the second case, and a more marked
+benefit in the third, if the load assumed to be a maximum
+were exceeded, or if the composite bar were tested to destruction;
+as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment
+as to how far this reserve of strength may be considered of
+value.</p>
+
+<p>If, instead of simply adding section to the bar, some part
+of the constant load is put upon the new section by the
+manner of attachment, the combination will, of course, be
+more effective.</p>
+
+<p>To apply these considerations and illustrate the way in
+which the two methods of adding flange section work out
+when reduced to figures, the case will be supposed of a girder
+6 feet deep, carrying a load of which one-third is dead and
+two-thirds live. To the flanges of this girder are added
+plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the
+girder before strengthening is liable, the depth remaining
+substantially unaltered. With dead load only the original
+section would be stressed to 2&middot;3 tons per square inch, the
+new section being then unstressed. Under full load the
+new and old material take 3&middot;1 tons per square inch additional,
+making the modified stress on the original section
+5&middot;4 tons per square inch, as against 7 tons; or a reduction
+of 22 per cent. This compares with 33 per cent., the relief
+due to 50 per cent. increase of flange area under ordinary
+conditions of stress distribution.</p>
+
+<p>Let the second method of strengthening the girder now
+be considered, using, for purposes of comparison, the same
+total amount of new material to increase the girder depth by
+an addition to the top flange. This section will be equal to<span class="pagenum"><a name="Page_115" id="Page_115">[115]</a></span>
+the area of one flange, which, though it may be applied in
+many different ways, giving a greater or a less increase to the
+depth, would probably be used in some
+such manner as that shown in <a href="#Fig64">Fig. 64</a>,
+increasing the effective depth for live-load
+stress by nearly 10 inches.</p>
+
+<div class="figcenter"><a name="Fig64" id="Fig64"></a>
+<img src="images/illo127.png" alt="" width="125" height="494" />
+<p class="caption"><span class="smcap">Fig.</span> 64.</p>
+</div>
+
+<p>The added material will, as in the
+previous case, leave the dead-load stress
+unaltered, or 2&middot;3 tons per square inch.
+The stress in the bottom flange due
+to live load will, however, now be 4&middot;1
+tons per square inch, making a total
+stress of 6&middot;4 tons per square inch,
+against 7 tons&mdash;the original stress.
+The reduction here is 8 per cent.
+only, as compared with 12 per cent.,
+the relief due, under ordinary conditions,
+to an increase of effective depth
+from 6 feet to 6 feet 10 inches, and by
+the use of additional material, equal,
+as before, to one-half of the total
+flange areas before the alteration.</p>
+
+<p>The effect on the top flange need
+not be here gone into in detail, but it
+may be said that, owing to the increase
+of gross section and of depth,
+the ultimate stresses of both the new
+and old material are greatly less than
+as given for the bottom flange.</p>
+
+<p>Girders strengthened by the first
+of these two methods would, it is probable,
+if tested to destruction, give
+results more nearly in accord with the actual percentage
+increase of flange section, plastic deformation of the metal,<span class="pagenum"><a name="Page_116" id="Page_116">[116]</a></span>
+before failure, tending to reduce the differences of stress on
+the new and old material of the sections.</p>
+
+<div class="figcenter"><a name="Fig65" id="Fig65"></a><a name="Fig66" id="Fig66"></a>
+<img src="images/illo128.png" alt="" width="350" height="470" />
+<p class="caption"><span class="smcap">Figs.</span> 65 and 66.</p>
+</div>
+
+<p>Web members of lattice girders may, if weak, sometimes
+be dealt with by the introduction of supplementary bars,
+parallel to and between the old members, or by the addition
+of strips or angles to the existing diagonals. The treatment
+will be largely influenced by the nature of the old detail,
+which may lend itself to some one arrangement much better
+than to any other.</p>
+
+<p>End riveting of web members may, if it has become
+loose, be dealt with by simply rhymering the holes a size
+larger, and re-riveting in the best manner, if the stresses are
+not excessive; or it may be necessary to devise some additional
+attachments by which new rivets are brought into use
+(see <a href="#Fig65">Figs. 65 and 66</a>). The effective relief due to supplementary<span class="pagenum"><a name="Page_117" id="Page_117">[117]</a></span>
+rivets will be influenced by similar considerations
+to those governing increase of section.</p>
+
+<div class="figcenter"><a name="Fig67" id="Fig67"></a>
+<img src="images/illo129.png" alt="" width="450" height="251" />
+<p class="caption"><span class="smcap">Fig.</span> 67.</p>
+</div>
+
+<div class="figcenter"><a name="Fig68" id="Fig68"></a>
+<img src="images/illo130.png" alt="" width="450" height="264" />
+<p class="caption"><span class="smcap">Fig.</span> 68.</p>
+</div>
+
+<p>Old structures are very frequently deficient in bracing,
+which may, in such cases, be advantageously introduced;
+or girders individually weak may be rendered collectively
+efficient by suitable bracing. In considering the advisability
+of this, however, the case should be viewed with regard to
+the possible effects of such members, as already dealt with
+in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders
+may have the effect, under live load, of increasing the stress
+on the outer girders due to twisting of the structure as a whole,
+though the inner girders will, except for full loading of the
+whole bridge, be advantaged as to stress values, and in any
+event bettered by being held up to their work. The effect
+upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations
+the detail should be schemed with special care to
+ensure simplicity in execution, smith&#8217;s work being rigorously
+avoided. A good arrangement for supplementary bracing
+between plate-girders, which gives little trouble in carrying
+out, is shown in <a href="#Fig67">Fig. 67</a>; or where the stiffeners of such girders<span class="pagenum"><a name="Page_118" id="Page_118">[118]</a></span>
+are in line across the bridge, the detail given in <a href="#Fig68">Fig. 68</a> may
+involve less expenditure. Difficulties may be experienced in
+riveting, unless great care is taken in the positioning of rivets.
+Fitting-bolts are only to be relied upon as such, if they really
+justify the name; they are, though easy to specify, by no
+means easy to secure under the conditions of practical work.
+Weak cross-girders may make alterations&mdash;in some cases
+considerable&mdash;necessary, to rectify the defect of strength.
+The removal of old girders to make room for new is seldom
+resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders
+between the old in cases where there is no plated floor to
+make the work difficult. By this method there is, of course,
+an increase of appreciable amount in the dead load carried
+by the main girders, which would in many instances be
+objectionable. With deep and heavy main girders, having
+plate webs, cross-girders may be strengthened by improving
+the end connections by suitable gussets, and attachment to
+good vertical stiffeners, the fixity of the ends thus aimed at
+being assured by overhead struts or girders, from one main
+girder to its fellow, at intervals apart well considered with
+reference to the horizontal strength of the top flanges, the<span class="pagenum"><a name="Page_119" id="Page_119">[119]</a></span>
+whole thus making a closed frame, as shown in <a href="#Fig69">Fig. 69</a>.
+The method appears feasible, but it should be stated that
+the author has not known it to be applied in its entirety as
+a means of strengthening an old floor.</p>
+
+<div class="figcenter"><a name="Fig69" id="Fig69"></a>
+<img src="images/illo131.png" alt="" width="450" height="280" />
+<p class="caption"><span class="smcap">Fig.</span> 69.</p>
+</div>
+
+<p>A simple and very common device consists in substituting
+for the ordinary cross-sleeper road, where this exists, stout
+timber longitudinals under the rails, which have, where the
+cross-girders do not exceed 5 feet centres, a marked distributive
+effect, tending to reduce the maximum load upon any
+individual girder. With a similar object, trough girders
+containing longitudinal timbers are sometimes adopted where
+the depth available is not enough to enable sufficiently stiff
+timbers to be used alone. In either case the object sought
+is the same&mdash;to modify the effect of the heavier wheel loads
+upon isolated cross-girders. When the spacing is so close
+as 4 feet, the beneficial result of this treatment is considerable,
+but at 8 feet centres it can have but a moderate effect
+where timbers alone are used.</p>
+
+<p>Occasionally, for long cross-girders, a distributing girder
+is placed, with the same intent, in the 6 feet way, its function
+being limited to this use only if the depth and strength are<span class="pagenum"><a name="Page_120" id="Page_120">[120]</a></span>
+sufficiently small to serve this object alone, as distinct from
+the case in which it becomes a carrying girder transferring
+load to the abutments. As a distributor simply, the girder
+has to equalise the bending moments amongst the cross-girders,
+to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous
+to alteration, for a position of the wheel loads such that the
+heaviest comes upon a centre cross-girder, the mean of these
+moments will, when compared with that for each girder,
+show the difference to be induced as a result of introducing
+the distributor. These differences of moment render necessary
+at the centre of the cross-girders reactions upwards
+or downwards, as the case may be, of amounts competent
+to induce moments below the inner rails equal to these
+differences.</p>
+
+<p>It is these reactions which must be provided by the distributing
+girder at a moderate stress, and without flexure of
+such an amount as sensibly to modify the reactions. The
+greatest section necessary at any one point may then be
+adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no
+harm in a little excess in a case of this kind, the total cost
+being but little affected by some small addition to the weight,
+where labour upon the site is so considerable an item as in
+work of this description. The ends of the distributing girder
+should be carried on to the abutments or piers to ensure
+adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at
+an early stage, by boning or by levelling, the condition of
+the cross-girders as to uniformity of heights, as this may affect
+the length most suitable for separate sections. Between the
+underside of the distributor and the cross-girder tops there
+will commonly be spaces of varying amounts, which should
+be filled by packings to fit, rather than by pulling the work<span class="pagenum"><a name="Page_121" id="Page_121">[121]</a></span>
+together by force, introducing undesirable stresses of uncertain
+amount.</p>
+
+<p>In the earlier remarks upon the strengthening of bridgework
+by the use of new material, it has been assumed that
+the modulus of elasticity of the new metal is similar to that
+of the old; it may, however, as in cases where wrought-iron
+work is reinforced by additions in steel, be necessary to
+take the difference of elastic properties into account, with
+which object the new section should be multiplied by a
+quantity (greater or less than unity) inversely proportional to
+the higher or lower modulus of the new material, that is to
+say, by</p>
+
+<p class="formula"><span class="division"><span class="num">E of old material</span><span class="denom">E of new material</span></span></p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span></p>
+
+<h2>CHAPTER XI.<br />
+<span class="chaptitle">STRENGTHENING OF RIVETED BRIDGES BY CENTRE
+GIRDERS.</span></h2>
+
+<p>The addition of distributing girders, described in the last
+chapter, as a means of strengthening a bridge floor, while
+sufficient in many cases so far as the cross-girders are concerned,
+does not in any appreciable way assist the main
+girders. When for a two-line bridge, having outer main
+girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders
+may be used, placed either above or below the cross-girders,
+on the centre line of the bridge.</p>
+
+<p>There are two principal ways in which such a girder may
+be brought into use; the easier, but generally less economical,
+is by making a simple attachment to the cross-girders,
+the old girder work still taking the whole dead load. By this
+method the new girder does no work but carry itself till the
+live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the
+second method is to make the connection adjustable, so that
+a part of the floor weights may be imposed upon the new
+girder as an initial load. In doing this the old outer girders
+will rise slightly, being relieved of stress, and the cross-girders
+also lifted at the middle, whilst the new girder is
+depressed as the load is brought upon it. With some part
+of the live load a very considerable proportion of the total
+may in this way be carried by a centre girder of moderate
+section. The whole question, by either method, turns upon<span class="pagenum"><a name="Page_123" id="Page_123">[123]</a></span>
+deflections; and it is in determining the relative movements
+of the girders that the problem chiefly lies.</p>
+
+<p>It is convenient first to determine the percentage of load
+relief to be effected in the main girders, as to which it is to
+be observed that as this relief (distributed) is induced by
+the upward reaction of the new girder acting at the centre
+of the cross-girders, the stress relief of these will, as a rule,
+greatly exceed that of the outside girders. For the generality
+of cases, it may be taken that the relief suitable for the
+outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress
+in these to a greater degree.</p>
+
+<p>If, however, it be thought desirable to check this, it may
+be done by considering a cross-girder subject to its dead and
+live loads acting downwards, and to reactions at the centre
+and ends. At the centre the reaction will be the load of
+which the two main girders are relieved on a length equal to
+the pitch of the cross-girders, or as here given<span class="nowrap">:&mdash;</span></p>
+
+<p class="numform"><a name="Form1" id="Form1"></a><span class="formula"><i>c</i> &times; <i>t</i> &times; P = reaction at centre</span>
+<span class="number">(1)</span></p>
+
+<p><i>c</i> being the percentage of relief; <i>t</i> the total load per foot run
+of the bridge; and P the pitch of cross-girders. The live
+loads carried by the cross-girders are for this purpose taken
+at per foot run, as for the main girders. With these data
+it will be easy to construct a diagram of moments, making
+it evident whether the relief proposed for the main girders
+will give a sufficient percentage of relief to the floor beams.</p>
+
+<p>Granting that this proportion has been decided, and
+dealing first with the case in which the centre girder is
+simply attached to the cross-girders, and takes no dead load
+other than its own weight, then the live load carried by the
+outside girders, and previously borne wholly by them, will
+be reduced by the amount it is intended to transfer to the
+centre girder, and will become</p>
+
+<p class="numform"><a name="Form2" id="Form2"></a><span class="formula">L<sub class="lg"><i>l</i></sub> - (<i>c</i> &times; L<sub class="lg"><i>t</i></sub>) = live load on outer girders</span>
+<span class="number">(2)</span></p>
+
+<p><span class="pagenum"><a name="Page_124" id="Page_124">[124]</a></span></p>
+
+<p>L<sub class="lg"><i>l</i></sub> being the total live load, and L<sub class="lg"><i>t</i></sub> the total dead and live
+load carried by the bridge. From this the deflection of the
+outer girders corresponding to this modified live load may
+be derived.</p>
+
+<div class="figcenter"><a name="Fig70" id="Fig70"></a>
+<img src="images/illo136.png" alt="" width="550" height="251" />
+<p class="caption"><span class="smcap">Fig.</span> 70.</p>
+</div>
+
+<p>It is next necessary to ascertain the vertical movement,
+commonly a depression, of the cross-girders at the centre
+relative to their ends, when subject to the running load only,
+and supported at the middle and ends, the centre reaction
+being obtained as before indicated <a href="#Form1">(1)</a>. This movement
+will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the
+upward flexure of the girder due to the centre reaction,
+considered as separate effects. Stress values having been
+estimated for the two conditions, these results may readily
+be deduced by simple flexure formul&aelig;, observing that while
+the curve of moments due to live load sufficiently approximates
+to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter
+&#8220;<a href="#Page_85">Deflections</a>,&#8221; the flexure due to the centre reaction will be
+but 0&middot;80 of that which corresponds to the same stress for
+distributed loading. Or, the curve assumed by the girder
+under live load may be plotted by a method to be later
+explained.</p>
+
+<p><span class="pagenum"><a name="Page_125" id="Page_125">[125]</a></span></p>
+
+<p>The sum of the movements now determined&mdash;that is,
+the live-load deflection of the outer girders, and depression,
+as is commonly the case, of the cross-girders&mdash;will give the
+extreme depression (marked <i>m</i> in <a href="#Fig70">Fig. 70</a>), from the dead-load
+condition of the middle cross-girders, when supported
+to the extent desired by a centre girder whose proportions are
+not yet known, but which, carrying the required percentage
+of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the
+flanges of the new girder, governed by this flexure, will for
+a plate girder be</p>
+
+<p class="numform"><a name="Form3" id="Form3"></a><span class="formula"><span class="division"><span class="num">D &times; C &times; <i>m</i></span>
+<span class="denom">S<sup>2</sup></span></span> = <i>f</i>, unit stress on gross section</span>
+<span class="number_up">(3)</span></p>
+
+<p>D and S being, as before (see &#8220;<a href="#Page_85">Deflections</a>&#8221;), the depth and
+span respectively in feet, C a constant, <i>m</i> the deflection in
+inches, and <i>f</i> the stress per square inch on the gross section
+of flange.</p>
+
+<p>The gross area A, of the flange, is given by</p>
+
+<p class="numform"><a name="Form4" id="Form4"></a><span class="formula"><span class="division"><span class="num">S &times; <i>c</i> &times; L<sub class="lg"><i>t</i></sub></span>
+<span class="denom">8 &times; D &times; <i>f</i></span></span> = gross area of flange</span><span class="number_up">(4)</span></p>
+
+<p><i>c</i> &times; L<sub class="lg"><i>t</i></sub>, being, as in <a href="#Form2">(2)</a>, the load transferred to and carried
+by the centre girder.</p>
+
+<p>The actual stress in the flanges will, of course, be greater
+by an amount due to the girder&#8217;s own weight; but this does
+not affect the question of relief. For any ordinary case the
+stress per square inch will be low; but it will manifestly be
+useless to assume a greater stress with a view to economy, as
+the effect of reducing the section will simply be to make the
+girder too flexible, thus causing it to be less effective than
+primarily intended. If, as is seldom the case, there is
+freedom as to the depth of girder permissible, it is evident
+the unit stress may be made a condition, and the depth<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span>
+deduced by a suitable modification of formula <a href="#Form3">(3)</a>; the
+relief desired being in this way equally well assured. Indeed,
+in the rare instances in which any depth may be
+adopted, this method is&mdash;contrary to the general rule&mdash;distinctly
+economical, particularly if the girder may be placed
+below the cross-girders, which simply rest upon it, without
+elaborate attachments.</p>
+
+<div class="figcenter"><a name="Fig71" id="Fig71"></a>
+<img src="images/illo138.png" alt="" width="550" height="259" />
+<p class="caption"><span class="smcap">Fig.</span> 71.</p>
+</div>
+
+<p>Considering now the second method of applying centre
+girders by which the new girder is made initially to carry
+part of the dead load, by adjustment, it will at once be
+recognised as a more complex matter. The measure of
+relief by which the old girderwork shall benefit need not
+be affected by the method of applying the centre girder,
+and may be decided on the principles already considered.
+The outer girders carrying a reduced load, when the bridge
+is fully loaded, and the cross-girders being in part supported
+at their centres in the manner already described, will give a
+resulting depression <i>m</i> (see <a href="#Fig71">Fig. 71</a>) of the centre cross-girders,
+below the original dead-load position, of a similar
+amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre
+girder, which may be designed to carry the required percentage<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span>
+of the total bridge loads with the maximum stress
+and depth, as conditions, leaving the initial dead load and
+necessary adjustments to be ascertained. This is the common
+case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.</p>
+
+<p>The centre girder of fixed depth being then required to
+carry a definite load at a definite flange stress, will deflect a
+definite amount at this stress. If this deflection equalled
+the extreme depression <i>m</i> of the old girder work, no adjustment
+would be necessary, the centre girder then carrying no
+initial dead load, as by the first method; but for centre
+girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally
+being small, and in order to ensure that the new girder shall
+do its full work, some dead load must be put upon it. In the
+act of adjustment the cross-girders must be lifted and the
+centre girder depressed, till the joint movement equals the
+excess <i>s</i> of the centre girder deflection over <i>m</i>, when the
+new girder will carry the proper amount of initial load, and
+upon further deflection under live load give the full measure
+of relief. The amount of &#8220;lift&#8221; or upward flexure of the
+old girder work, and the depression or &#8220;drop&#8221; of the new
+girder, during adjustment, will depend upon relative stiffness,
+and may be ascertained as follows<span class="nowrap">:&mdash;</span></p>
+
+<p>For unit reactions at the centre of the cross-girders the
+upward flexure of these may be ascertained, as also the
+upward flexure of the two outer girders when subject to
+forces of the same total amount (one-half to each) applied
+at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are
+subject to unit lifting forces; similarly, the depression of
+the centre girder for unit loads applied at the cross-girders
+may be determined. There will then be known the movements<span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span>
+upwards and downwards of the old and new work
+when being drawn together by unit forces applied as stated.</p>
+
+<p>If</p>
+
+<table class="formula nowrap" summary="Table page 128">
+
+<tr>
+<td class="left"><i>l</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">lift due to unit loads,</td>
+</tr>
+
+<tr>
+<td class="left"><i>l<sub class="lg">t</sub></i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">total lift due to adjustment,</td>
+</tr>
+
+<tr>
+<td class="left"><i>d</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">drop due to unit loads,</td>
+</tr>
+
+<tr>
+<td class="left"><i>d<sub class="lg">t</sub></i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">total drop due to adjustment,</td>
+</tr>
+
+<tr>
+<td class="left"><i>s</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">deflection excess = gross adjustment,</td>
+</tr>
+
+</table>
+
+<p>there will then be</p>
+
+<p class="formula"><span class="division"><span class="num"><i>d</i></span>
+<span class="denom"><i>l</i> + <i>d</i></span></span> &times; <i>s</i> = <i>d</i><sub class="lg"><i>t</i></sub>,</p>
+
+<p>total drop of centre girder under adjustment,</p>
+
+<p class="formula"><span class="division"><span class="num"><i>l</i></span>
+<span class="denom"><i>l</i> + <i>d</i></span></span> &times; <i>s</i> = <i>l</i><sub class="lg"><i>t</i></sub>,</p>
+
+<p>total lift of centre cross girders under adjustment,</p>
+
+<p class="formula"><span class="division"><span class="num"><i>d</i><sub class="lg"><i>t</i></sub></span><span class="denom"><i>d</i></span></span> &times; unit load =</p>
+
+<p>initial load put upon centre girder at each cross-girder.</p>
+
+<p>The rise of the two outer girders for upward forces
+together equal to those depressing the centre girder may
+readily be deduced.</p>
+
+<div class="figcenter"><a name="Fig72" id="Fig72"></a>
+<img src="images/illo141.png" alt="" width="350" height="321" />
+<p class="caption"><span class="smcap">Fig.</span> 72.</p>
+</div>
+
+<div class="figcenter"><a name="Fig73" id="Fig73"></a>
+<img src="images/illo142.png" alt="" width="500" height="258" />
+<p class="caption"><span class="smcap">Fig.</span> 73.</p>
+</div>
+
+<p>The act of adjustment may conveniently be effected by
+the arrangement shown in <a href="#Fig72">Fig. 72</a>, in which each cross-girder
+is hung up at its centre by four bolts. At the middle of
+the centre girder the total amount to be screwed up will be
+that corresponding to the deflection excess <i>s</i>, but towards
+the ends this amount decreases, and may advantageously be
+represented by a diagram as <a href="#Fig73">Fig. 73</a>, in which, if <i>s</i> represents
+to scale the amount to be screwed up at a centre cross-girder,
+the corresponding amounts for other girders may be read off
+direct. It will be apparent that it must be necessary to<span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span>
+place the centre girder at such a height as to leave a space
+between the old and the new work greater than the amount
+to be screwed up, this excess clearance being ultimately filled
+by a packing.</p>
+
+<p>The precautions to be observed in carrying out this
+kind of work, and the practical methods of adjustment
+adopted by the author after some little experience, may here
+be given.</p>
+
+<p>Great care is necessary at the outset to ascertain the true
+spacing of the cross-girders, to ensure that the bolt-holes in
+the bottom flange of the centre girder shall come where
+desired. The fixing of the cross-girder brackets also needs
+close attention to avoid after trouble, the bolt-holes in the
+brackets being preferably drilled on the site after fixing.
+It will, for masonry abutments, be necessary to fix bedstones
+to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span>
+leave the stones liable to settle slightly when the full load
+is carried. To eliminate the bad effect of this upon the
+ultimate adjustment, and to take up any initial set of the
+new girder work, which would be prejudicial in the same
+way, it is desirable, the centre girder being in place, to screw
+up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it
+is convenient to prepare, for use at the bridge, a diagram
+somewhat similar to <a href="#Fig73">Fig. 73</a>, giving the amount by which
+the new and old work are to be brought together at each
+cross-girder, with the number of turns for each nut to effect
+this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is
+repeated as often as necessary, and so managed as to bring
+all up proportionately to the final requirement, keeping tally
+with chalk marks over each cross-girder as a check. The
+preliminary screwing up should be conducted with little less
+care than that adopted for the later adjustment, to avoid
+damage to the old work. This later adjustment having in
+due course been effected, it is then necessary to measure for
+packings to fill the spaces remaining between the old cross-girders<span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span>
+and the new centre girder. These spaces should be
+callipered at each of the four corners, care being taken to
+avoid after-confusion. The measurements ascertained will,
+however, be too great for the finished packings, as an allowance
+of not less than <sup>1</sup>&#8260;<sub>10</sub> inch (total), will commonly be
+wanted to cover irregularities in the surfaces. The packings,
+having been prepared and checked, may be slipped into
+place after slacking all the bolts a small amount to permit
+this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last
+operation.</p>
+
+<p>As a check upon the calculations and adjustment, the
+&#8220;lift&#8221; of the outer girders and cross-girders, and the &#8220;drop&#8221;
+of the centre girder may be observed by levelling. For this
+purpose the author has used a staff of inches divided into
+tenths, with which, and a good level, very accurate readings
+may be taken for short distances.</p>
+
+<p>No reference has been made to the effect of skew in a
+bridge on the above methods, the explanation given applying
+rather to bridges square on plan. The influence of skew on
+the load distribution will largely be a matter of detailed
+calculation. The flexure of the girders may also be sensibly
+affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to
+modify the amount of screwing up during adjustment, which
+may be better understood by reference to <a href="#Fig74">Fig. 74</a>, and comparing
+it with <a href="#Fig73">Fig. 73</a>, the adjustment diagram for a square
+bridge.</p>
+
+<p>To illustrate how these methods of strengthening work
+out, and compare as to weights of centre girders required,
+the case has been assumed of a wrought iron bridge of 60-feet
+span, having outer girders 5 feet deep, of 39 square inches
+gross flange area; and cross-girders, at 8-feet centres, 27-feet
+span, 1 foot 9 inches deep, with a gross flange area of twenty<span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span>
+square inches. The dead load and live load on either road
+are each 1&middot;75 tons per foot run.</p>
+
+<p>The stress in the outer girders previous to the alteration
+being 6 tons per square inch gross, it is desired to relieve
+this to the extent of 33 per cent. by a steel centre girder.
+In the table here given the quantities given in italics are
+fixed as primary conditions<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Centre Strengthening Girders for 60-ft. Span.</span></p>
+
+<table class="nowrap" summary="Table page 132">
+
+<tr class="bt bb">
+<th class="center br">&mdash;</th>
+<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Stress<br />Unknown.</th>
+<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Depth<br />Unknown.</th>
+<th colspan="2" class="center padl1 padr1">Adjust-<br />ments<br />Unknown.</th>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Outer Girder.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Deflection under modified live load</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1">in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Lift of adjustment</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;153</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Cross Girders.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depression under live load&mdash;modified conditions of support</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Extreme depression (<i>m</i>)</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1 br">&#8222;</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1 br">&#8222;</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Lift of adjustment (cross-girder only)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;095</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Total lift of adjustment (<i>l<sub class="lg">t</sub></i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;248</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Centre Girder.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depth</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>3&middot;5 ft.</i></td>
+<td colspan="2" class="center bot padl1 padr1 br">8&middot;2 ft.</td>
+<td colspan="2" class="center bot padl1 padr1"><i>3&middot;5 ft.</i></td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Unit stress on gross section (ex girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">2&middot;14 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>5&middot;0 tons</i></td>
+<td colspan="2" class="center bot padl1 padr1"><i>5&middot;0 tons</i></td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Total deflection (ex girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">&middot;55 in.</td>
+<td colspan="2" class="center bot padl1 padr1 br">&middot;55 in.</td>
+<td class="left bot padl2 padr0">1&middot;28</td>
+<td class="center bot padl0 padr1">in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Deflection excess (<i>s</i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;73</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depression, or &#8220;drop&#8221; of adjustment (<i>d<sub class="lg">t</sub></i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;482</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Gross area of flange</td>
+<td colspan="2" class="center bot padl1 padr1 br">105 sq. in.</td>
+<td colspan="2" class="center bot padl1 padr1 br">19&middot;2 sq. in.</td>
+<td colspan="2" class="center bot padl1 padr1">44&middot;5 sq. in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Weight</td>
+<td colspan="2" class="center bot padl1 padr1 br">20 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br">10&middot;4 tons</td>
+<td colspan="2" class="center bot padl1 padr1">11&middot;4 tons</td>
+</tr>
+
+<tr class="bb">
+<td class="left top padl1 padr1 br wrappable">Net flange stress (including girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">3&middot;19 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br">6&middot;87 tons</td>
+<td colspan="2" class="center bot padl1 padr1">6&middot;94 tons</td>
+</tr>
+
+</table>
+
+<p>Girders subject to distributed load are treated as having<span class="pagenum"><a name="Page_133" id="Page_133">[133]</a></span>
+uniform stress, but where this is not strictly the case, as in
+some light girders, it will be necessary to take the fact into
+account. For centre girders of wrought iron, and a unit
+stress on the gross section of 4 instead of 5 tons, the girder
+weights are between 9 and 10 per cent. greater.</p>
+
+<div class="figcenter"><a name="Fig74" id="Fig74"></a>
+<img src="images/illo145.png" alt="" width="500" height="237" />
+<p class="caption"><span class="smcap">Fig.</span> 74.</p>
+</div>
+
+<p>In the above treatment of the application of centre
+strengthening girders there is a source of error which should
+be touched upon. If, under live load, the centre girder
+deflects more than the outer girders, as it commonly will,
+there must be a want of uniformity in the behaviour of the
+cross-girders, those near the abutments being more relieved
+than the estimated amount of relief of those at the centre,
+which will have less than that intended; but the reduction
+of stress in the cross-girders will generally be so considerable
+that any such ambiguity of excess or defect is commonly
+unimportant; the effect of this also upon the main girders
+is much less than might be supposed, being, for the third of
+the cases just given, about 2<sup>1</sup>&#8260;<sub>2</sub> per cent. excess for the centre
+girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as
+approximate only. It is possible to eliminate some part of<span class="pagenum"><a name="Page_134" id="Page_134">[134]</a></span>
+the error by lifting the end cross-girders during adjustment,
+a less amount than that given by the diagrams, <a href="#Fig73">Figs. 73</a> and
+<a href="#Fig74">74</a>, taking care that the centre girder is depressed its full
+amount by lifting the centre cross-girders a little more; this
+refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.</p>
+
+<p>Particulars are here given of five ordinary cases, comparing
+the calculated and observed results of adjustment. The
+operation of levelling was conducted by a quick-eyed and
+capable assistant, who was not made acquainted with the
+results expected, in order to avoid any sub-conscious tendency
+to match the calculated figures<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Examples of Centre Girder Adjustments.</span></p>
+
+<table class="nowrap" summary="Table page 134-135">
+
+<tr class="bt bb">
+<th class="center br">&mdash;</th>
+<th colspan="2" class="center padl1 padr1 br">Calculated.</th>
+<th colspan="2" class="center padl1 padr1">Observed.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th colspan="2" class="center padl1 padr1 br">in.</th>
+<th colspan="2" class="center padl1 padr1">in.</th>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 1.&mdash;56-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;82</td>
+<td colspan="2" class="center padl1 padr1">&middot;84</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;23</td>
+<td colspan="2" class="center padl1 padr1">&middot;22</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;20</td>
+<td colspan="2" class="center padl1 padr1">&middot;10 and &middot;13</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 2.&mdash;57-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;50</td>
+<td colspan="2" class="center padl1 padr1">&middot;50</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;18</td>
+<td colspan="2" class="center padl1 padr1">&middot;20</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;11</td>
+<td colspan="2" class="center padl1 padr1">&middot;08 and &middot;10</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 3.&mdash;67-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;70</td>
+<td colspan="2" class="center padl1 padr1">&middot;75</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;15</td>
+<td colspan="2" class="center padl1 padr1">&middot;17</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;10</td>
+<td colspan="2" class="center padl1 padr1">&middot;09</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 4.&mdash;68-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;70</td>
+<td colspan="2" class="center padl1 padr1">&middot;65</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;20</td>
+<td colspan="2" class="center padl1 padr1">&middot;18</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;13</td>
+<td colspan="2" class="center padl1 padr1">&middot;14</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 5.&mdash;52-<i>Ft. and</i> 28-<i>Ft. Spans continuous.<span class="pagenum"><a name="Page_135" id="Page_135">[135]</a></span></i></td>
+</tr>
+
+<tr class="bb">
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1 br">Long<br />Span.</th>
+<th class="center padl1 padr1 br">Short<br />Span.</th>
+<th class="center padl1 padr1 br">Long<br />Span.</th>
+<th class="center padl1 padr1">Short<br />Span.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1">in.</th>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td class="center padl1 padr1 br">&middot;28</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;29</td>
+<td class="center padl1 padr1">..</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of centre girder</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;04</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1">&middot;03</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders (centre of spans)</td>
+<td class="center padl1 padr1 br">&middot;17</td>
+<td class="center padl1 padr1 br">&middot;09</td>
+<td class="center padl1 padr1 br">&middot;15</td>
+<td class="center padl1 padr1">&middot;13</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1">..</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl1 padr1 br">Depression of outer girder</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;01</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1">negli-<br />gible.</td>
+</tr>
+
+</table>
+
+<p>The method of calculation adopted for these cases was
+not precisely that given, though depending upon the same
+broad principles. The first cannot be considered a good
+example. The last, having continuous girders, of course
+needed special treatment.</p>
+
+<p>Of about seventeen bridges strengthened in the manner
+described, the effect generally was satisfactory, in reducing
+deflection and vibration; but in two cases of small span,
+owing probably to settlement of bedstones, the results were
+not so good.</p>
+
+<p>From first to last the work of putting in a centre girder
+takes some little time, owing to the slow progress generally
+made in fixing the brackets, preparing packings, etc. The
+cost of a typical case was about 23 per cent. of the cost of a
+new superstructure, with a 30 per cent. relief of stress.</p>
+
+<div class="figcenter"><a name="Fig75" id="Fig75"></a>
+<img src="images/illo148.png" alt="" width="500" height="303" />
+<p class="caption"><span class="smcap">Fig.</span> 75.</p>
+</div>
+
+<div class="figcenter"><a name="Fig76" id="Fig76"></a>
+<img src="images/illo149.png" alt="" width="500" height="283" />
+<p class="caption"><span class="smcap">Fig.</span> 76.</p>
+</div>
+
+<p>A special case of strengthening by a centre girder, having
+considerable interest, may be here referred to. The primary
+idea involved was not the author&#8217;s. The bridge dealt with
+has already been noticed under &#8220;<a href="#Page_34">Bracing</a>&#8221; and a section,
+before alteration, shown in <a href="#Fig26">Fig. 26</a>. The span being 85
+feet, there was no room for a centre girder of sufficient depth
+above the cross-girders and between the roads, nor was it
+considered economical to place the girder wholly below the<span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span>
+floor, because of the costly staging this would have necessitated
+for erection purposes, the height above ground level
+being very great. A girder was therefore designed, having
+open latticing at an angle of 60 degrees, with a bottom boom
+to be below the cross-girders, the top being as high above
+the rails as could be permitted (see <a href="#Fig75">Figs. 75</a> and <a href="#Fig76">76</a>). A
+temporary boom was arranged at the intersection of diagonals,
+the lower boom proper not being fixed till the girder
+having been lifted into place, with the diagonal members
+passing between the cross-girders, allowed this to be done.
+The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being
+then 2 inches. The permanent boom was then put in place,
+and the girder restored as nearly as was practicable to the
+camber it was intended to have when complete, but without
+throwing, during the process, any improper loads upon the
+old work.</p>
+
+<p>The lower boom being finally riveted up, the cross-girders
+were made to bear upon it by suitable packings. There
+were, in addition to the new girder, two stiff frames between
+the old main girders, to which the new was secured.</p>
+
+<p><span class="pagenum"><a name="Page_137" id="Page_137">[137]</a></span></p>
+
+<p>The girder was designed with the intention that under
+dead load only the cross-girders should just rest, but throw
+no weight, upon the new work, the latter assisting to carry
+live load only. The floor beams being of small span, and
+securely riveted to the old girder tops, the centre girder was
+required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion,
+the three points of support of the cross-girders thus not
+altering their relative levels. That this resulted was evident
+from the fact that, previous to connecting the cross-frames
+to the centre-girder, the work being otherwise complete, a
+space between the two of about <sup>1</sup>&#8260;<sub>2</sub> inch, afterwards filled by
+a packing, showed no alteration, the closest measurement
+failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be
+expected, very marked.</p>
+
+<p>In the conduct of that class of strengthening work which
+has been dealt with in this chapter, it is essential, in the
+author&#8217;s judgment, that the man responsible for the detailed
+calculations and design should himself see the operations of<span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span>
+adjustment carried out, or delegate it only to one equally
+familiar with the requirements.</p>
+
+<p>Before dismissing the subject, it will be well to refer to
+a method of approximately determining flexure curves, of
+occasional use in dealing with centre girder or similar questions.
+The figure assumed is plotted to an exaggerated scale,
+with which object the actual radius of curvature at points
+along the girder&#8217;s length are first ascertained by the formula</p>
+
+<p class="formula"><span class="division"><span class="num">E &times; D</span><span class="denom"><i>f</i> &times; 2</span></span> = R, radius of curvature in feet,<br />
+</p>
+
+<p>and the radius of curvature for the diagram by</p>
+
+<p class="numform"><a name="Form5" id="Form5"></a><span class="formula">12 &times; R &times; F<sup>2</sup> = <i>r</i>, radius for plotting, in inches</span>
+<span class="number">(5)</span></p>
+
+<p>E being the modulus of elasticity, D the girder&#8217;s depth in
+feet, <i>f</i> the mean of the extreme flange stresses per square
+inch of gross area, and F the fraction indicating scale as <sup>1</sup>&#8260;<sub>48</sub>,
+where <sup>1</sup>&#8260;<sub>4</sub> inch = 1 foot. The curve, being plotted, shows by
+direct scaling the movement of any point relative to its
+original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn
+with the help of template curves, or even set out as pieces of
+&#8220;straight.&#8221;</p>
+
+<p>When the curve is laid down so that its chord equals the
+span to scale, the method involves an error of excess in the
+resulting deflection or droop which is as much as 7 per cent.
+when the mean radius for plotting equals the span as drawn,
+or when the droop of curve approaches one-eighth of the
+span. As the exaggeration of curvature is made less pronounced,
+this error rapidly diminishes, till for a droop of
+about one-sixteenth the percentage is one-fourth part of that
+above given. This excess in the droop of curve may be
+amended by the following expression<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula">droop - <span class="fsize150">(</span><span class="division"><span class="num">droop<sup>3</sup></span><span class="denom">chord<sup>2</sup></span></span>
+&times; 3&middot;73<span class="fsize150">)</span> = corrected droop, or deflection.</p>
+
+<p><span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span></p>
+
+<p>For some purposes it may be preferable to amend the
+radii for plotting, so that the curve, as laid down, shall be<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span>
+correct, which may be effected by the formula here given, to
+be applied to each value of r, as first ascertained<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><i>r</i> + <span class="fsize150">(</span><span class="division"><span class="num">chord<sup>2</sup></span>
+<span class="denom"><i>r</i></span></span> &times; &middot;0625<span class="fsize150">)</span> = corrected plotting radius.</p>
+
+<p>If, however, the length of curve is made equal to the
+span (the chord then being less), and the radii for plotting
+as given by <a href="#Form5">(5)</a> are used, the result will for most purposes
+be sufficiently precise, though there will now be an error of
+a contrary kind, which, for a curve having a droop of one-eighth,
+will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described
+by Professor Fleeming Jenkin in the article &#8220;Bridges&#8221; of
+the &#8220;Encyclop&aelig;dia Britannica,&#8221; but without corrections.</p>
+
+<p>A careful comparison of results by the above means, with
+those calculated, shows that with good draughtsmanship they
+may be relied upon for considerable accuracy. Equally
+applicable to girders of varying depth and flange stress,
+they have also a limited use in cases of continuity.</p>
+
+<div class="figcenter"><a name="Fig77" id="Fig77"></a><a name="Fig78" id="Fig78"></a>
+<img src="images/illo151.png" alt="" width="264" height="550" />
+<p class="caption"><span class="smcap">Figs.</span> 77 and 78.</p>
+</div>
+
+<p><a href="#Fig77">Figs. 77 and 78</a> illustrate the deflection and stress diagrams
+for the cross-girders of the bridge supposed to have
+been strengthened by a centre-girder, when under the
+influence of live load and a centre reaction of a definite
+amount. As a matter of convenience, each radius length
+has been halved, before correction, so that the resulting
+droop of the curve is twice the true amount.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span></p>
+
+<h2>CHAPTER XII.<br />
+<span class="chaptitle">CAST-IRON BRIDGES.</span></h2>
+
+<p>Cast Iron as a material for bridges has of late years fallen
+into disrepute. It is now entirely tabooed by the Board of
+Trade for railway under-bridges, unless of arched construction.
+This condemnation of cast iron followed, and was
+apparently the result of, an accident which occurred to an
+under-bridge on one of the southern lines, which bridge had
+already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good,
+inasmuch as it led to a thorough overhaul of all railway
+under-bridges in this country, and the renewal of a great
+number no longer in a condition suited to the carriage of
+heavy or of passenger traffic; yet there is little doubt
+that, in the author&#8217;s judgment, many excellent cast-iron
+bridges were then removed at considerable cost, to be replaced
+by others of wrought iron or steel, which will not last
+so long as many of those displaced had done, or would still
+have lasted had they not been dismantled.</p>
+
+<p>The earlier cast-iron bridges were commonly made of
+cold-blast iron, a material of such strength and toughness as
+to give an extraordinary amount of trouble in breaking up
+the heavier parts, when the time arrived to do this, and with
+which material ordinary hot-blast iron is not to be compared
+for reliability.</p>
+
+<div class="figcenter"><a name="Fig79" id="Fig79"></a>
+<img src="images/illo154.png" alt="" width="500" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 79.</p>
+</div>
+
+<p>As illustrating the very considerable stress to which cast
+iron may be subjected, without of necessity leading to any
+mishap, two cases may be cited. The first, a bridge of 32<span class="pagenum"><a name="Page_142" id="Page_142">[142]</a></span>
+feet effective span, carrying two lines of way, each pair of
+rails being supported upon Barlow rails, forming the bridge
+floor, the ends resting upon the bottom flanges of inverted
+<span class="lettsymb">T</span>-shaped girders, 2 feet 3 inches deep, as shown in <a href="#Fig79">Fig. 79</a>.</p>
+
+<p>The extreme fibre stress works out at 2&middot;9 tons per square
+inch in tension, and 5&middot;9 tons per square inch compression,
+calculated as it would be in ordinary office work; but for
+the actual loads, at a span as above, exceeding the clear span
+by 6 inches only, and without regard to the effects of eccentric
+application of the load. The girders when taken out showed
+upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be
+too strongly condemned, notwithstanding that in this case no
+ill resulted. It is evident that a piece of the lower flange
+being broken out from this cause, as occasionally happens,
+might so reduce the section as to result in complete failure.</p>
+
+<div class="figcenter"><a name="Fig80" id="Fig80"></a><a name="Fig81" id="Fig81"></a>
+<img src="images/illo155.png" alt="" width="500" height="382" />
+<p class="caption"><span class="smcap">Figs.</span> 80 and 81.</p>
+</div>
+
+<p>The second example is that of a small railway under-bridge
+of two spans, continuous over the central pier, each
+span being 16 feet 6 inches. The rails were supported upon
+longitudinal timbers lying within trough-shaped girders, as
+shown in <a href="#Fig80">Figs 80 and 81</a>.</p>
+
+<p>The stress over the pier, in the extreme fibres of the top
+flange, is estimated at 4&middot;7 tons per square inch in tension,
+but it should be noted that the effect of the timber longitudinal
+and rail has been neglected in arriving at this result,<span class="pagenum"><a name="Page_143" id="Page_143">[143]</a></span>
+which might possibly on this account be reduced to near
+3 tons per square inch.</p>
+
+<p>The case is noticeable because no evidence of high stress
+was apparent. The author saw nothing to suggest sinking
+of the central pier, the effect of which, within limits, would
+be to further reduce the stress as calculated; but it is quite
+possible some slight settlement had occurred; this, as the
+spans were so small, would have a sensible effect. While too
+much reliance should not, it is clear, be placed upon any
+estimated result about which there is a lingering doubt, it
+should be remarked that, as it would be necessary the pier
+should sink <sup>3</sup>&#8260;<sub>16</sub> of an inch, for each ton of reduced stress, it
+is not probable that the results quoted are in excess to any
+material degree; they are, indeed, more probably low, as no
+notice has been taken of impact.</p>
+
+<p>Though cast-iron girders for railway under-bridges are
+now prohibited in this country for new works, there are still
+uses to which they may be applied, and it may be well to
+insist that girders of this material should be fairly loaded, the<span class="pagenum"><a name="Page_144" id="Page_144">[144]</a></span>
+weight being brought upon them in such a way that there
+shall be no serious secondary stress, such as arises when wide
+flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking
+down under a load fairly applied. Preference is now given
+to steel or wrought iron for columns; while this is often
+quite justifiable, there remain many cases in which nothing
+better need be desired for this purpose than good cast iron,
+provided only that the column be loaded in a suitable
+manner&mdash;i.e., axially, and that the arrangement and details
+of the super-structure are such that there shall be no cross-breaking
+efforts, or rocking of the column due to temperature
+or other causes; unless, indeed, such cross-breaking or
+rocking is definitely taken into account in designing the work.
+The same care observed in the detailing of cast-iron work
+that is not infrequently taken in the design of structures
+made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with
+the advantage of greater resistance to rust, and a reduced
+cost in maintenance.</p>
+
+<p>Good cast iron is, in fact, when used with discretion, a
+most excellent material, popular predjudice notwithstanding.
+The oldest metallic bridge in this country at the present
+moment is of that metal.</p>
+
+<p>The one chief respect in which cast iron is at a disadvantage
+compared with wrought iron or steel is that it does not
+give premonitory warning of failure&mdash;it remains intact, or it
+breaks. The indications of weakness, which may be read by
+an experienced inspector of other metallic bridges, are in
+a great measure absent. There is also an objection which
+may exist, but is to be avoided by good design and care in
+the foundry&mdash;viz., internal stress due to unequal cooling.
+In extreme cases this may lead to fracture before the work<span class="pagenum"><a name="Page_145" id="Page_145">[145]</a></span>
+has left the maker&#8217;s hands, but it can only occur by neglect
+of ordinary precautions.</p>
+
+<div class="figcenter"><a name="Fig82" id="Fig82"></a><a name="Fig83" id="Fig83"></a>
+<img src="images/illo158a.png" alt="" width="550" height="265" />
+<p class="caption"><span class="smcap">Figs.</span> 82 and 83.</p>
+</div>
+
+<p>In a case which has already been referred to in the
+chapter on &#8220;<a href="#Page_73">Deformations</a>,&#8221; <a href="#Page_80">page 80</a>, an outer rib of a
+cast-iron arch fractured near the crown after fifty-four years&#8217;
+use. Owing to the nature of the design, and the fact that
+the near abutment had closed in slightly, bringing the linear
+arch of necessity near the lower edges of the arch segment
+in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces,
+at the upper edge where fracture commenced. The result
+was very far from explaining the occurrence of the break,
+but an examination of the details shown in <a href="#Fig82">Figs. 82 and 83</a>
+will make it apparent that, in addition to the tensile stress, as
+calculated, there was probably a severe initial stress of the
+same character due to irregular cooling in the foundry half a
+century before. The sum of these stresses, it is suggested,
+placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent
+either by producing a small further settlement of the foundations,
+of which the author saw no evidence, or, as is more
+probable, the attachment of a rope to this rib for the purpose
+of keeping a barge in position, which certainly did occur,
+gave the arch rib just such an additional strain as to result
+in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The
+inner ribs were of a much less objectionable section.</p>
+
+<div class="figcenter"><a name="Fig84" id="Fig84"></a>
+<img src="images/illo158b.png" alt="" width="550" height="182" />
+<p class="caption"><span class="smcap">Fig.</span> 84.</p>
+</div>
+
+<p>Cast-iron arches, though still allowed by the Board of
+Trade rules, are, indeed, liable to be seriously affected by
+settlement, or yielding of the abutments, unless hinges at the
+crown are introduced. As an instance of this may be quoted
+a bridge of some 45 feet span, in which the arches were cast
+in two pieces abutting, and very efficiently bolted together at
+the crown, the springing and vertical abutment member of<span class="pagenum"><a name="Page_146" id="Page_146">[146]</a></span>
+the spandrel being bolted and built solidly into heavy
+masonry. The arch sank at the crown, caused by, or itself
+the cause of, a movement of the abutment, with the result
+that the lower bolts at the crown joint broke away, rupturing
+the casting, as shown in <a href="#Fig84">Fig. 84</a>. The arch must then have
+acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if
+a proper hinge had originally been provided. The break
+happened to occur so as to leave a sufficiently good bearing<span class="pagenum"><a name="Page_147" id="Page_147">[147]</a></span>
+face at the crown; there was, indeed, no tendency for one
+surface to slide upon another; but in the accidental fracture
+of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.</p>
+
+<p>A second case of very much the same character has also
+been under the author&#8217;s observation, though in this the ends
+of the spandrels were not built into the brickwork of which
+the abutments were composed. Other instances of fracture
+either in the arch proper or in the spandrel work, have come
+under notice, though particulars cannot now be adduced;
+but the examples cited are by themselves sufficient to justify
+the conclusion that it is imprudent to construct a cast-iron
+arch without a central pin or its equivalent, unless the abutments,
+being exceptionally well founded, may be relied upon
+as free from any liability to move. It is, however, to be
+borne in mind that movement in the abutments of a small
+arch of any given absolute amount is more injurious than the
+same amount of movement in the abutments of large arches
+of similar design, so that what may be negligible in the latter
+case would perhaps be destructive in the former.</p>
+
+<p>To the absence of ductility and liability to initial stress
+must be added yet another disadvantage to which cast-iron
+work is prone&mdash;viz., the possibility of concealed defects,
+blow-holes or cold-shuts; these in good foundry practice are
+not very likely to occur, but, as they are possible, cannot
+be overlooked in considering the suitability of cast iron for
+bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks
+by way of qualification, the author reiterates his opinion that
+there is still a use for cast iron in bridgework.</p>
+
+<p>With respect to the repair of cast-iron bridges, but little
+is to be said; the possibilities in this direction are very
+limited. Occasionally it may be desired to deal with the
+fracture of some member in the spandrel bracing of an arch,<span class="pagenum"><a name="Page_148" id="Page_148">[148]</a></span>
+when it is commonly sufficient, and even preferable, to limit
+the repair work to confining the fractured parts in such a
+way as to prevent displacement.</p>
+
+<p>Rarely it may happen that an arch fractures as a result
+of settlement, or other movement, when, if it is decided that
+safety of the structure is not imperilled, it will in this case
+also be preferable to confine the parts simply by flitch-plates
+or other contrivance, with no attempt rigidly to make good
+the break, the consequences of which treatment would
+probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable,
+though something may occasionally be done by the
+negative process of lightening the dead load, or by remodelling
+the permanent way. Arches may, however, be
+rendered much more reliable by the introduction of suitable
+bracing where this is either wanting or inefficient.</p>
+
+<p>In scheming such additions it is desirable to arrange for
+as little drilling of the old work as is possible; where this
+cannot be altogether avoided, the position of the holes should
+be carefully chosen with regard to the effect they may have
+upon the strength of the old work.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_149" id="Page_149">[149]</a></span></p>
+
+<h2>CHAPTER XIII.<br />
+<span class="chaptitle">TIMBER BRIDGES.</span></h2>
+
+<p>Timber bridges, though probably the most ancient in
+type, are yet the least durable in any particular instance.
+The perishable nature of the material when used for exposed
+construction renders it peculiarly liable to develop defects
+which quickly put a limit to the life of the structure. In
+addition to decay in the body of the main members&mdash;which
+may perhaps be long delayed, so that a simple beam bridge
+may last for many years&mdash;there is in more complex designs
+decay at connections and joints, which proves very detrimental
+to the integrity of the whole. Water running upon
+the surface of a member gravitates to its lower end, and, if
+there be a joint or other connection, settles there, to be productive
+of lasting mischief. From this cause, together with
+a very common deficiency of bearing surface relative to the
+forces to be met, the joints soon develop some movement;
+working of the structure commences under passing loads, its
+final destruction being then a question of time only. Each
+joint is, in fact, in timber bridge construction a source of
+serious weakness to a degree which has no parallel in well-designed
+metallic bridges.</p>
+
+<p>Wrought-iron straps to confine the ends of raking
+members, or for other uses, are liable to crush into the wood,
+and bolts are apt to enlarge the hole through which they
+pass. Wood keys, where these are introduced to prevent one
+timber from sliding upon another, are also prone to develop
+cracks in the main members, and fibre crippling from excess<span class="pagenum"><a name="Page_150" id="Page_150">[150]</a></span>
+of stress. All these defects are, however, in timber-work
+more easily defined than efficiently remedied, as it is barely
+practicable for any but the harder woods to ensure, for heavy
+loads, a sufficiency of bearing surfaces.</p>
+
+<p>The most readily detected evidence of deterioration in
+timber bridges is the sag of its bearing members, or trusses,
+for the simple reason that if there is no local trouble at the
+joints, there will probably be no appreciable drop at the
+centre of the span. The existence of such a depression
+may, however, be caused in rare instances by the spread
+of the supporting piers or abutments, particularly in
+the case of beams trussed by end diagonal rakers and
+having no tie.</p>
+
+<p>Bridges formed of deep trusses, with the road upon the
+top, are sometimes found to be wanting in lateral bracing,
+the result of which is that the main trusses go out of line,
+leaning considerably one way or the other, being checked
+only by such rigidity as the joints and floor-beam attachments
+may have, with possibly some assistance from the end connections
+of the span.</p>
+
+<p>The decay of piles where entering the ground or water
+is, of course, a fruitful source of trouble, as also is the sinking
+of piles, where these are insufficient in number, or have
+not been well driven in the first place.</p>
+
+<p>A vital difficulty with timber structures generally is the
+uncertainty that will commonly exist as to how far decay
+extends in those cases where it has started. Timber does
+not necessarily show upon its surface the evidences of internal
+rotting. Memel timber may, indeed, be sometimes found
+to have become thoroughly unreliable, yet showing no sign
+of this upon its painted surface. By sounding the wood
+with a hammer, or by probing, its condition may commonly
+be ascertained. In cases of doubt, an auger-hole will make
+it clear as to whether the interior be good or otherwise, as<span class="pagenum"><a name="Page_151" id="Page_151">[151]</a></span>
+to the particular parts tested; but only as to those parts,
+leaving it a matter of guesswork as to the remainder.</p>
+
+<div class="figcenter"><a name="Fig85" id="Fig85"></a>
+<img src="images/illo164a.png" alt="" width="550" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 85.</p>
+</div>
+
+<p>A railway bridge having many of the defects which have
+been indicated may be quoted as an example. This structure
+crossed a canal, supported upon piles, some of which were in
+water, others carrying land spans. The canal span consisted
+of four trusses, one under each rail, or nearly so, framed in
+the manner shown in <a href="#Fig85">Fig. 85</a>, precise details not, however,
+being now available. The trusses, apart from deflection
+under live load, sagged considerably&mdash;in one instance,
+4<sup>1</sup>&#8260;<sub>2</sub> inches; one inside truss was also leaning towards the
+centre line of the bridge as much as 3 inches. One raker,
+or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections
+and joints were also in a bad condition. The vertical
+tie-bolts of the main trusses were all slack. The piles
+generally, many of which were badly decayed, had sunk and
+inclined towards one end of the bridge about 4 inches in
+7 feet of height, the ground being soft and unreliable.</p>
+
+<p>Movement under a passenger train crawling over the
+bridge was very appreciable, but not startling. There had
+been introduced, from time to time, additional timbers and
+iron ties, with the object of rendering the spans more reliable,
+but leaving it somewhat difficult to determine the function
+of the several members. The bridge was, of course, reconstructed.</p>
+
+<div class="figcenter"><a name="Fig86" id="Fig86"></a>
+<img src="images/illo164b.png" alt="" width="550" height="182" />
+<p class="caption"><span class="smcap">Fig.</span> 86.</p>
+</div>
+
+<div class="figc550"><a name="Fig87" id="Fig87"></a><a name="Fig88" id="Fig88"></a>
+<img src="images/illo165.png" alt="" width="550" height="209" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 87.</span> <span class="right49"><span class="smcap">Fig.</span> 88.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 87. and <span class="smcap">Fig.</span> 88.</p>
+</div>
+
+<p>An instance may here be cited showing how badly distorted
+a timber structure may become without actually
+falling. The bridge referred to consisted of three spans of
+29 feet, each span having two trusses, between which ran
+a colliery tramroad, 1-foot 6-inch gauge; the corves running
+upon this, at 4 feet 6 inch centres, weighed, when full,
+about 10 cwt. each. The trusses were badly out of shape,
+the centre span having sagged 5<sup>1</sup>&#8260;<sub>2</sub> inches, with one truss of<span class="pagenum"><a name="Page_152" id="Page_152">[152]</a></span>
+the same span nearly 10 inches out of line at the centre.
+This little bridge, of which some details are shown in <a href="#Fig86">Figs.
+86</a>, <a href="#Fig87">87, and 88</a>, had been in use about twenty years.</p>
+
+<div class="figcenter"><a name="Fig89" id="Fig89"></a>
+<img src="images/illo166.png" alt="" width="600" height="212" />
+<p class="caption"><span class="smcap">Fig.</span> 89.</p>
+</div>
+
+<p>A third case which may be named is that of a road bridge,
+about 12 feet wide, crossing by thirteen spans a shallow river
+liable to floods. The construction was of a simple character,
+as indicated in <a href="#Fig89">Fig. 89</a>, and consisted of piles supporting
+trussed beams, which had sagged in some instances over<span class="pagenum"><a name="Page_153" id="Page_153">[153]</a></span>
+2<sup>1</sup>&#8260;<sub>2</sub> inches. The bridge had, some years previous to the
+author&#8217;s inspection, been heavily repaired, many new strut
+and stretching pieces having been introduced, the piles also
+being reinforced or renewed. Five years before, a traction
+engine, said to weigh 5 tons, had passed across the bridge in
+safety; but the author noticed that a coal wagon, which,
+with the horse, weighed about 50 cwt., when walked slowly
+over set up much movement. This bridge had been in use
+nearly thirty years, and was very much out of line from end
+to end.</p>
+
+<p>Though timber bridges cannot at the best be considered
+durable, yet, by attention to certain points in design and
+construction, their length of life may be materially enhanced.<span class="pagenum"><a name="Page_154" id="Page_154">[154]</a></span>
+Every cut across the grain may be considered an element of
+weakness by exposing the material to quicker decay, for which
+reason the number of ends, or of joints, should be reduced
+to a minimum. An additional reason for reducing the
+number of joints or other
+connections is the liability
+of these to develop movement,
+as already stated, the
+yield of any one joint, being
+the cause of movement in
+others, which might, but for
+this, have remained close.
+These considerations lead
+to the conclusion that fewness
+of parts is, in timber
+construction, as in structural
+work generally, an excellent
+principle to observe. Mortising,
+elaborate scarf joints,
+recessing, or any cutting into
+the timber which is not essential,
+should be avoided, the
+simplest forms of connection
+being preferable, if at
+all suitable. If a step or
+butt surface is wanted for
+any member, it is commonly
+better to provide this by a
+cleat or other added piece,
+rather than by cutting into the timber butted against.</p>
+
+<p>A complicated joint formed in the body of main timbers
+can only be renewed by renewal of the timber itself, whereas
+by the method indicated the joint is readily tightened, or
+re-made, without involving the main member. Bearing<span class="pagenum"><a name="Page_155" id="Page_155">[155]</a></span>
+surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake
+of bearing surface in the holes, and reduction of any
+liability to bend under cross-stress. In trusses of the
+form shown in <a href="#Fig85">Figs. 85</a> and <a href="#Fig86">86</a>, it is desirable to introduce
+diagonal members in the middle bay, even though it
+may appear that the stiffness of the main beams is sufficient
+to render this unnecessary as a matter of strength, as without
+these there is apt to be, under rolling load, a slight
+distortion, leading to working of the joints and free entry
+of moisture. Lateral bracings should also, for much the
+same reasons, be introduced, even though they may not
+appear necessary in the new structure, with joints all close
+and effective.</p>
+
+<p>Projecting ends of timbers should be carried out well
+beyond the requirement of strength or bearing, in order to
+ensure a liberal margin for that decay in the end fibres which
+commonly develops. Timbers resting upon abutments, or
+running into confined spaces, should be arranged for free
+ventilation and ready drying. Occasionally joints at the
+lower ends of timbers are protected by lead or zinc flashings
+to prevent water running into them, a method which should
+have some protective value. Whatever measures may be
+adopted, whether in the design or execution of timber bridge-work,
+will, however, be but little effective, if the timber itself
+is not good of its kind, and well seasoned.</p>
+
+<p>Creosoting to be useful should be thorough and something
+more than skin deep. The timber itself should be well dried
+before treatment.</p>
+
+<p>The repair of timber bridges very largely consists in the
+renewal of decaying timbers, where this is practicable, or in
+adding supplementary pieces where the old cannot conveniently
+be displaced. Joints may be tightened up by
+hard-wood wedges, properly secured to prevent slacking back,<span class="pagenum"><a name="Page_156" id="Page_156">[156]</a></span>
+all bolts being also screwed up tight, perhaps some additional
+being introduced.</p>
+
+<p>Piles standing in water, which have decayed, may be
+strengthened by driving other piles between the old, or on
+either side, but not of necessity opposite to them, and by
+means of waling timbers bolted to the old piles, put in a
+position to take load, either by the walings resting upon
+their tops, or being bolted to them. Piles decayed where
+entering solid ground may generally be strengthened by
+bolting on supplementary timbers to reach well above and
+below the decayed part, or by cutting out the bad length,
+introducing a new piece, and fishing the butt-joints in a
+proper manner. But all remedial measures have generally
+to be considered with reference to cost, as compared with
+the probable increase of life of the structure. With a bridge
+in an advanced state of decrepitude, such repairs may prove
+anything but economical, and at the best defer reconstruction
+but a very moderate length of time.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_157" id="Page_157">[157]</a></span></p>
+
+<h2>CHAPTER XIV.<br />
+<span class="chaptitle">MASONRY BRIDGES.</span></h2>
+
+<p>Masonry bridges, in which description it is intended to
+include structures both in stone and brick, are, when well
+built, amongst the most durable and long-suffering of any
+which come under the care of a maintenance engineer; yet
+when developing the faults peculiar to their kind, they may
+be the occasion of much anxiety, and render necessary frequent
+inspection, or even continuous watching.</p>
+
+<p>Apart from decay of mortar or material, defects may very
+commonly be traced to the foundations, or to earth-slips.
+Sinking, when uniform, may be quite harmless, though
+possibly inconvenient; irregular sinking of piers or abutments
+is quite a different matter. It is, however, remarkable
+to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and
+kind which would be fatal to the connections of metallic
+bridgework is endured by bridges of stone or brick; not, it
+may be, without damage, yet with no occasion for alarm.
+The superstructure of metallic bridges may often, however,
+be restored to the true level before the mischief has become
+serious, whereas in the case of masonry arches this is not
+practicable.</p>
+
+<p>Spreading of the abutments is very seldom the cause of
+any great injury to an arch, though it is common enough to
+find old and flat arches slightly down at the crown; but the
+contrary case of abutments closing in is not very unusual
+when these are high, or terminate a viaduct over a deep<span class="pagenum"><a name="Page_158" id="Page_158">[158]</a></span>
+valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected;
+or, if the arches are very solid and heavy, the abutment may
+slide forward at the base, with no sensible reduction of the
+opening.</p>
+
+<p>When a viaduct connects the two ends of a high embankment,
+it may happen that the end piers are not clear of the
+embankment slope, in which event a pier may, should the
+bank slip, move with it, as to that part not in solid ground;
+with the result, in a bad case, that it is broken across and the
+superstructure imperilled.</p>
+
+<div class="figcenter"><a name="Fig90" id="Fig90"></a>
+<img src="images/illo170.png" alt="" width="450" height="248" />
+<p class="caption"><span class="smcap">Fig.</span> 90.</p>
+</div>
+
+<p>A case of abutment movement is illustrated in <a href="#Fig90">Fig. 90</a>,
+which represents the end arch of a masonry viaduct, one
+abutment of which had moved forward in the manner
+already referred to. From the springing upwards the arch
+retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the
+movement became pronounced, heavy timber centering was
+introduced, with the object of preventing any mishap, the
+damaged portions being ultimately cut out and made good.
+The structure was thirty-five years old.</p>
+
+<p>The practical utility of stop piers in long arched viaducts
+is, perhaps, rather in checking movement of the tops of piers<span class="pagenum"><a name="Page_159" id="Page_159">[159]</a></span>
+under moving load than in arresting actual failure of a series
+of arches. That the tops of piers do move very sensibly
+need not be doubted. The author has attempted to measure
+this in the case of piers about 60 feet to the springing, by
+means of a theodolite placed below, but has reached no more
+definite result than that a movement existed, of which he
+was not able to determine the amount. If in a viaduct some
+arches are more heavily loaded than others, each spreading
+slightly, the end piers of the group will move amounts which
+together equal the sum of the individual span spreads, with
+a tendency in the arches beyond those of the group overloaded
+to rise.</p>
+
+<p>This rocking may be detrimental both to the piers and
+arches, and helps to account for the disintegration of mortar
+in arches and piers, which not infrequently happens. The
+soffits will sometimes be seen with a thick incrustation of
+lime, which has washed out of the joints, or from limestone
+ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that
+pieces of stone or brick will drop out, necessitating repair at
+heavy expense, of which scaffolding is commonly a large
+part.</p>
+
+<p>Tall piers may be found badly out of the upright due to
+sinking of foundations. A marked case of this kind came
+under the author&#8217;s notice&mdash;a viaduct of fifteen semicircular
+arches, in which, though many piers were wanting in truth,
+one in particular was about 1 foot 4 inches out of vertical,
+making one side of the shaft plumb, and doubling the normal
+batter of the other. Inquiry showed that in this instance
+the pier had never been upright from its earliest history
+dating back thirty-six years. This makes clear the desirability,
+to avoid hasty conclusions, of ascertaining, when it is
+possible to do so, the complete record of any structure.</p>
+
+<p>A bridge fifty-eight years old, of three skew spans, carrying<span class="pagenum"><a name="Page_160" id="Page_160">[160]</a></span>
+a railway over a canal, and having somewhat flat brick
+arches with stone quoins upon low piers, developed the somewhat
+unusual defect, as to the centre arch, of splitting along
+its length for about 10 feet, parallel to and some 7 feet from
+one face. In this case there was reason to believe that there
+had been considerable local settlement of the piers on that
+side of the bridge. The arches were otherwise in bad condition,
+the brickwork poor, and the mortar decayed. Each
+arch was down at the centre, and displayed a fault not
+unusual where bad brickwork joins up to good cut stonework,
+the quoins showing a tendency to separate from the
+brick rings. Below the bridge were coal-workings.</p>
+
+<p>Brick arches built in parallel rings sometimes separate
+one ring from the other, demonstrating the known propriety
+of bonding the rings together properly, and of carrying the
+arch round, when building, at its full thickness.</p>
+
+<div class="figcenter"><a name="Fig91" id="Fig91"></a>
+<img src="images/illo172.png" alt="" width="550" height="245" />
+<p class="caption"><span class="smcap">Fig.</span> 91.</p>
+</div>
+
+<p>An instance of bridge failure from a somewhat peculiar
+cause may be quoted as of some interest, largely because the
+structure was very ancient, having been in existence some
+400 years. This bridge, carrying a road, was of the type
+usual in old masonry bridges over a river, having small
+arches, thick piers, and solid backings to the arches. Two<span class="pagenum"><a name="Page_161" id="Page_161">[161]</a></span>
+flood-openings at one end had, by sinking and want of care,
+become partly closed. The centre arch had, however, been
+widened about 140 years previously. During a severe flood,
+the swollen river, overflowing its banks, trespassed upon a
+timber yard a little above bridge, and washed down into the
+stream a large quantity of sawn timber; this, unable to get
+through the main arch with freedom, compacted into a serious
+obstruction. The flood water, thus checked in its passage,
+seems to have scoured below the timber, and robbed the piers
+of such support as they formerly had (see <a href="#Fig91">Fig. 91</a>). The
+bridge stood in this condition till the water lowered, when
+the middle part of the structure broke up, and subsided into
+the hole which had been washed out. But for the monolithic
+character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers
+stood had been partly undermined
+for very many years.
+The case is instructive, as
+showing how a slight accident&mdash;powerless
+by itself
+to work mischief&mdash;may be
+very damaging when allied
+with so powerful an agent
+as running water.</p>
+
+<div class="figcenter"><a name="Fig92" id="Fig92"></a>
+<img src="images/illo173.png" alt="" width="300" height="351" />
+<p class="caption"><span class="smcap">Fig.</span> 92.</p>
+</div>
+
+<p>The enduring character
+of even the roughest class
+of masonry arch, if only
+the material be good and
+abutments stable, is shown
+when it becomes necessary to destroy old work of this
+character. <a href="#Fig92">Fig. 92</a> represents a short length of &#8220;cut and
+cover&#8221; arching in process of demolition, just before it
+fell in. The masonry was of hard sandstone rubble and
+had been cut away, as shown, till at the point A only a very<span class="pagenum"><a name="Page_162" id="Page_162">[162]</a></span>
+small piece of the arch remained, when the length finally
+broke up and dropped. Arches have commonly a great
+reserve of strength; tunnel linings are, indeed, often badly
+out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed
+or bulged, to serve the purpose intended.</p>
+
+<p>Though the equilibrium of masonry arches has been the
+occasion of much profound study, and the nicest calculation
+has sometimes been applied to the design of such work, yet
+it appears that when an arch is well backed up, the theoretical
+linear arch need have but little connection with the figure of
+the intrados; a statement consonant both with common-sense
+and the teachings of experience. With solid backing, this
+would indeed seem to be more important than any part of
+the arch ring below the top of the backing, the lower part
+of the ring serving chiefly to preserve the face of the solid
+work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure
+would seem to be inevitable. The masonry or brickwork
+does not always show evidence of damage, if the distortion
+has been slow; suggesting that structures of this kind have
+a power of accommodation with which they are not generally
+credited.</p>
+
+<p>A noticeable cause of deterioration of masonry structures,
+which may be quite independent of settlement, is serious
+vibration. This is well known in connection with church
+belfries, and is also locally apparent when telegraph or other
+poles are attached to masonry parapets. Vibration, when
+caused by heavy railway traffic, acting upon arches light or
+originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially
+built, and particularly those carrying ordinary roads,
+and not subject to much vibration, have great lasting powers,<span class="pagenum"><a name="Page_163" id="Page_163">[163]</a></span>
+if repaired with skill, or even let alone. Distortion of the
+arch may be quite consistent with practical stability, if the
+movement or decay with which it originated is not progressive,
+or has been arrested. In this connection a distinction
+is to be made between arches well backed, to which the foregoing
+remarks apply, and in which the two halves of each
+arch may act as separate monoliths meeting at the crown, and
+the case of a true arch ring independent of any outside resistance,
+such as backing or spandrels may give, and depending
+almost wholly upon the proper balance of its component
+voussoirs for its stability. With the latter class of structure
+no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way,
+and the work is dealt with judiciously, if at all. It must,
+however, be understood that there are limits as to what
+may be done effectively, short of rebuilding, in dealing with
+structures in which, perhaps, brickwork is rotten and mortar
+decayed and crumbling, the whole being little better than a
+broken mass of rubbish.</p>
+
+<p>In cases where it may be prudent to introduce safety
+centring, as in an instance already referred to, it is commonly
+expedient to refrain from causing this to take any sensible
+part of the load till all movement has ceased, the centres
+being at the outset largely precautionary. The requirement
+with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement
+is still going on, the effect may be to cause the arch to break
+up upon the centring, and precipitate repair work which
+might otherwise have been left to a more convenient time,
+when all movement had stopped or been checked by suitable
+measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt
+with piecemeal by cutting out the bad places, a small part<span class="pagenum"><a name="Page_164" id="Page_164">[164]</a></span>
+at a time, and making good. The work requires the greatest
+care of experienced men.</p>
+
+<p>Pointing masonry or brickwork is effective for little
+other than protective purposes, and to check further weathering;
+it has obviously no effect upon the interior work, and
+if made to cover up the evidences of internal decay, is even
+misleading and objectionable. In extreme cases it may be
+desirable to open out the road and deal with the filling, to
+relieve or to strengthen the outer spandrel walls, which sometimes
+bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise
+repairing solid backing, in which operations some regard
+must be had to the effect of the work upon the balance of
+the opposing halves of the arch.</p>
+
+<p>Of the different classes of masonry commonly used in
+bridgework, it may be well to remark that good coursed
+rubble, or preferably that variety bonding both vertically
+and horizontally, of a durable stone, perhaps quite unfit for
+any but rough dressing, may make a most lasting structure,
+the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from
+the block, probably along some line of relative weakness&mdash;there
+is no &#8220;nursing&#8221; of weak corners; whereas with stones
+reduced to a perfectly regular shape by chisel work, the
+plane surfaces and geometrical angles are made with partial
+regard only to the natural grain of the stone.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_165" id="Page_165">[165]</a></span></p>
+
+<h2>CHAPTER XV.<br />
+<span class="chaptitle">LIFE OF BRIDGES&mdash;RELATIVE MERITS.</span></h2>
+
+<p>The life of bridges of differing materials has been incidentally
+touched upon by the examples quoted, in dealing with
+each class of structure. It will be useful to recapitulate
+some of the facts adduced, and to compare the terms of life
+so far as they appear to be indicated; but in doing this it is
+necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history.
+The duration of any such structure may be limited by adverse
+conditions, peculiar to the case considered, by defects
+of design, material, or workmanship&mdash;present from the first&mdash;or
+by neglect, overloading, or accident, making up its later
+record.</p>
+
+<p>With the exception of timber structures, it is difficult to
+find any class of bridges furnishing examples which have
+reached the limit of life, independently of the evils named,
+and as a result of unavoidable decrepitude. There are none
+the less influences at work tending to this condition, and
+which it is too much to expect can in all cases be foreseen or
+completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and
+minor faults in design, which even in the most capable hands
+may be expected ever to fall short of perfection. At the
+best, then, the life of any structure, though long, must have
+a limit. With bridges of more average or inferior qualities
+the life may be positively short, even without the destructive
+influence of overloading.</p>
+
+<p><span class="pagenum"><a name="Page_166" id="Page_166">[166]</a></span></p>
+
+<p>Dealing with instances of metallic bridges, the adjacent
+table gives the time each had been in existence when removed,
+and some indication of the reason for its condemnation.
+Those marked with an asterisk were cases of pronounced high
+stress. From a study of the table it appears that in actual
+practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and
+thirty-six years; but these figures applied to this collection
+of cases only. It is to be remarked that many other bridges
+outlasted these, and are likely to continue reliable. These
+results show, then, no more than that some wrought-iron
+bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as
+indicating that the durability of such structures is by no
+means so limited as the table would suggest. It is to be
+observed that, as design and maintenance are now better and
+more generally understood than when experience was largely
+wanting, it is to be expected that later examples will show
+no such poor results.</p>
+
+<p>Of steel bridges little can be said, because of the limited
+time this material has been in use; but the generally acknowledged
+belief, quite in agreement with the author&#8217;s observation,
+that steel rusts more freely than wrought iron, suggests
+that such bridges will have a shorter lease of life, the more
+so that the surface-to-section ratio is also greater for higher
+unit stresses, though other adverse influences are much the
+same for one material as for the other.</p>
+
+<p>Of cast-iron structures but few cases have been given; of
+these, cast-iron arches have been noticed as developing defects
+which led to reconstruction, or to limiting the loads to be
+carried. Plain cast-iron girders, on the other hand, have
+never, under the author&#8217;s direct observation, been removed
+for any other reason than because they were cast iron, or
+from over-stress, due to the growth of loads; never from<span class="pagenum"><a name="Page_167" id="Page_167">[167]</a></span>
+defects or wasting, though it is not suggested no such cases
+exist. The author has no evidence which points to what
+may be the limit of life of a good cast-iron girder fairly
+treated.</p>
+
+<p class="center"><i>Examples of Life of Metallic Bridges.</i></p>
+
+<table class="nowrap" summary="Table page 167">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">Description.</th>
+<th colspan="2" class="center padl1 padr1 br">Span.</th>
+<th class="center padl1 padr1 br">Age.</th>
+<th class="center padl1 padr1 br">Defect.</th>
+<th class="center padl1 padr1">Reference.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1">ft.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">Years.</th>
+<th class="br">&nbsp;</th>
+<th>&nbsp;</th>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Wrought Iron.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">12</td>
+<td class="center padl1 padr1 br">Loose rivets</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">*Ditto</td>
+<td class="right padl1 padr1">35</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">12</td>
+<td class="center padl1 padr1 br">Ditto</td>
+<td class="left padl1 padr1"><a href="#Page_52">p. 52</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">55</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">14</td>
+<td class="center padl1 padr1 br">Rust. Distortion</td>
+<td class="left padl1 padr1"><a href="#Page_78">pp. 78</a> &amp; <a href="#Page_97">97</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Trough girders</td>
+<td class="right padl1 padr1">11</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">16</td>
+<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_50">p. 50</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">22</td>
+<td class="center padl1 padr1 br">Loose rivets</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Twin girders</td>
+<td class="right padl1 padr1">31</td>
+<td class="right padl1 padr1 br">6</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Weak. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_13">p. 13</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">35</td>
+<td class="right padl1 padr1 br">6</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Weak. Distorted.</td>
+<td class="left padl1 padr1"><a href="#Page_74">p. 74</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td class="right padl1 padr1">42</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_21">p. 21</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">72</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">29</td>
+<td class="center padl1 padr1 br">Weak. Loose rivets</td>
+<td class="left padl1 padr1"><a href="#Page_53">p. 53</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">47</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">24</td>
+<td class="center padl1 padr1 br">Distortion</td>
+<td class="left padl1 padr1"><a href="#Page_9">p. 9</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">32</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">32</td>
+<td class="center padl1 padr1 br">Rust. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_14">p. 14</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">*Ditto</td>
+<td class="right padl1 padr1">25</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">36</td>
+<td class="center padl1 padr1 br">Weak</td>
+<td class="left padl1 padr1"><a href="#Page_63">p. 63</a></td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Steel.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">*Trough girders</td>
+<td class="right padl1 padr1">15</td>
+<td class="right padl1 padr1 br">8</td>
+<td class="center padl1 padr1 br">32</td>
+<td class="center padl1 padr1 br">Weak. Rusted</td>
+<td class="left padl1 padr1"><a href="#Page_68">pp. 68</a> &amp; <a href="#Page_98">98</a></td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Cast Iron.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">*Girders</td>
+<td class="right padl1 padr1">32</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">36</td>
+<td class="center padl1 padr1 br">Weak</td>
+<td class="left padl1 padr1"><a href="#Page_141">p. 141</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Girders, cast-iron piles</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">44</td>
+<td class="center padl1 padr1 br">Ditto</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Arches</td>
+<td class="right padl1 padr1">45</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">55</td>
+<td class="center padl1 padr1 br">Crack. Settlement</td>
+<td class="left padl1 padr1"><a href="#Page_145">p. 145</a></td>
+</tr>
+
+<tr class="bb">
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">100</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">62</td>
+<td class="center padl1 padr1 br">Crack. Deformation</td>
+<td class="left padl1 padr1"><a href="#Page_80">pp. 80</a> &amp; <a href="#Page_145">145</a></td>
+</tr>
+
+</table>
+
+<p>With timber bridges the length of life appears to be about
+twenty-five years, but this is very largely dependent upon
+the question of maintenance, and may range from fifteen to
+thirty-five years. It is manifest that repairs, when extensive
+and consisting of the renewal of the more essential parts of<span class="pagenum"><a name="Page_168" id="Page_168">[168]</a></span>
+the structure, border upon reconstruction, and may be continued
+indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for
+railway bridges, be taken as stated, though for highway
+bridges possibly longer.</p>
+
+<p>Of masonry bridges little is to be said but that it is only
+in cases of bad work or material&mdash;with, perhaps, vibration
+or settlement&mdash;that these have a shortness of life comparable
+with that of defective metallic bridges. Where these adverse
+conditions obtain, heavy repairs may be necessary before the
+structure is many years old; but, under reasonably fair conditions,
+bridges of masonry may be expected to outlast structures
+in any other material. Apart from road-bridges which
+are admittedly long-lived, there are a large number of railway
+bridges and viaducts of masonry which, despite heavy loads
+and vibration, have been in use for the past seventy years.</p>
+
+<p>Dealing with the cost of maintenance, this with bridges
+of wrought iron or steel should result simply from scraping
+and painting, with such other incidental work as may be
+necessary on the subsidiary materials used in the structure.
+The cost of painting will vary with the height and character
+of the bridge, and the amount of scaffolding, if any, and
+may be from 5<i>d</i>. to 1<i>s</i>. or more per square yard; this if
+distributed over five years, a not unusual interval between
+each painting, works out at an appreciable figure, which may
+vary from one-third to one per cent. of the first cost, per
+annum. The yearly cost of painting steel-work will, for
+shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be
+necessary, repairs and possibly strengthening, which may
+raise the total cost of maintenance very considerably.</p>
+
+<p>Cast-iron bridges, being less liable to rust, cost less for
+painting than other metallic bridges; and if the cast iron is
+closed in by masonry, practically nothing; they do, indeed,<span class="pagenum"><a name="Page_169" id="Page_169">[169]</a></span>
+involve very little expenditure in the maintenance. Not
+being very amenable to repair or strengthening, cast-iron
+bridges commonly remain very much as built, or are reconstructed.</p>
+
+<p>The proper care of timber bridges may become costly as
+the structure gains in age, and soon grow to a very wasteful
+expenditure. This is evident when it is considered that
+repairs may be necessary after ten years, and that whatever
+may have been the cost of any part when new, it cannot be
+replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions
+to be observed in dealing with an old structure
+carrying its load. In addition to ordinary repairs, there will
+be paint or other protective coating to be applied, though
+this is not always done.</p>
+
+<p>The upkeep charges of masonry bridges will be practically
+nothing in favourable cases; but, on the other hand, where
+extensive repairs become necessary, may reach a considerable
+amount. Exceptional outlays are, however, infrequent, and
+may be spread over a large number of years, in those rare
+instances in which they become imperative.</p>
+
+<table class="nowrap" summary="Table page 169">
+
+<tr>
+<th class="center"><i>Durability.</i></th>
+<th class="center padl3 padr3"><i>Maintenance<br />Charges.</i></th>
+<th class="center"><i>First Cost.</i></th>
+</tr>
+
+<tr>
+<td class="left">Masonry</td>
+<td class="left padl3 padr3">Masonry</td>
+<td class="left">Timber</td>
+</tr>
+
+<tr>
+<td class="left">Cast Iron</td>
+<td class="left padl3 padr3">Cast iron</td>
+<td class="left">Masonry</td>
+</tr>
+
+<tr>
+<td class="left">Wrought iron</td>
+<td class="left padl3 padr3">Wrought iron</td>
+<td class="left">Steel</td>
+</tr>
+
+<tr>
+<td class="left">Steel</td>
+<td class="left padl3 padr3">Steel</td>
+<td class="left">Cast iron</td>
+</tr>
+
+<tr>
+<td class="left">Timber</td>
+<td class="left padl3 padr3">Timber</td>
+<td class="left">Wrought iron</td>
+</tr>
+
+</table>
+
+<p>For purposes of ready comparison, placing bridges of the
+materials under review in order of durability, they would
+appear as in column 1 of the table above; in order of low
+maintenance charges, generally as in column 2; and in order
+of low first cost, as in column 3. With respect to the question
+of first cost, the arrangement of the third column applies
+only to small bridges, say, up to 70-foot span; and, being<span class="pagenum"><a name="Page_170" id="Page_170">[170]</a></span>
+liable to variation with the conditions, is but approximately
+correct. The less costly descriptions of masonry are alone
+considered in this connection.</p>
+
+<p>It may be added that the total yearly charge of interest
+on first cost, redemption, and maintenance, appears to be for
+masonry bridges, about one-half only of the corresponding
+totals for bridges of wrought iron, steel, or timber; those of
+cast iron taking an intermediate place.</p>
+
+<p>Summarising the above considerations, and dealing with
+the relative merits of bridges in the different materials, it
+may be broadly stated that for conditions at all suitable
+nothing seems to be superior to masonry&mdash;including in
+this description first-class brickwork&mdash;whether for road or
+railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little
+affected by increase of loads. The mass of a masonry arched
+structure is so great, and the margin of strength commonly
+so liberal, that considerable increments of load may have but
+little effect upon the reliability of the structure.</p>
+
+<p>Cast iron has, for bridges of simple design, a strong claim
+to the second place, though its want of ductility is a demerit.
+It can, however, have but a limited use in bridge construction,
+being applicable only to small girder spans and skilfully-designed
+arched structures.</p>
+
+<p>For bridges of moderate span in which the question of
+cost does not control the matter, wrought iron should probably
+come next, steel being best reserved for those of a larger
+size, in which weight of the structure greatly affects economy.</p>
+
+<p>Timber may be regarded as a material rarely to be used
+in this country for structures to occupy a permanent place,
+unless for urgent economic reasons of the moment.</p>
+
+<p>While expressing this general view of the matter, it is to
+be admitted that the propriety of these conclusions is somewhat
+discounted by the difficulty there now is in obtaining<span class="pagenum"><a name="Page_171" id="Page_171">[171]</a></span>
+cast iron of the desired toughness, or wrought iron with
+promptitude and sufficient variety of section at a reasonable
+price.</p>
+
+<p>It is apparent, also, that the choice of material may be
+largely influenced&mdash;even determined&mdash;by considerations of
+headway, construction depth, or character of foundations; so
+that no very definite rules can be usefully laid down, though
+the adoption of unsuitable materials has not been so unusual
+as to make these suggestions altogether purposeless.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_172" id="Page_172">[172]</a></span></p>
+
+<h2>CHAPTER XVI.<br />
+<span class="chaptitle">RECONSTRUCTION AND WIDENING&mdash;CONCLUSION.</span></h2>
+
+<p>The need for the reconstruction of bridges, arising from
+various causes which have been treated in the preceding
+chapters, original weakness or faults in design, decay or defects,
+may also be caused by such extraneous considerations as the
+growth of loads, widening of the openings spanned, or improvement
+of the headway.</p>
+
+<p>In any case, a precise survey or measuring up of the
+structure and its immediate surroundings is required, in the
+execution of which the greatest care is desirable, and with
+respect to which it may be well to give a few hints.</p>
+
+<p>The surveying chain, when used, should be tested, the
+measure of accuracy required rendering this imperative in a
+degree peculiar to work of this class. Linen tapes should
+also be compared with a reliable steel tape, and used only
+where sufficiently accurate for the particular purpose. A
+careful and observant man may do very good work with a
+linen tape, making just that allowance in the sag of the tape
+which corrects for the inevitable stretch; but there is still
+some uncertainty involved in its use, and the author prefers
+to rely upon a steel tape, notwithstanding the inconvenience
+commonly experienced from its intractable nature and liability
+to damage.</p>
+
+<p>Instruments used must also be in the best adjustment;
+as errors, which in ordinary field work may not be of great
+importance, are inadmissible in bridge work.</p>
+
+<p>It is not necessary here to enter upon the methods of<span class="pagenum"><a name="Page_173" id="Page_173">[173]</a></span>
+small survey work, but it may be desirable to point out that
+abutment walls should be plumbed for verticality; girders,
+which are liable to be leaning, defined in position by reference
+to their bearings; and generally that it should never be taken
+for granted that there is truth in old work, or that this may
+be assumed as to line or level.</p>
+
+<p>In cases where disputes with any local authority as to
+headway are likely to arise, it is prudent to supplement the
+information as to level of soffits by rods cut to length in strict
+agreement with the clear height, before removing the old
+superstructure.</p>
+
+<p>It is apparent that in cases where the superstructure is
+already condemned, the detail measurements may be confined
+to that part of the structure which is to remain, securing
+only such information as to the work superseded which may
+be required in arranging for the new work.</p>
+
+<p>In taking particulars of skew bridges, needless as the
+warning may seem, it is yet necessary to remark that there
+may be right or left-hand skews which will not reverse.
+The author has known a disregard of this to make serious
+trouble in two instances.</p>
+
+<p>Dealing first with reconstruction of the superstructure of
+railway under-bridges, these, if small, may not give much
+trouble, though the demand for greater strength will, perhaps,
+involve some difficulty in working to the limiting construction
+depth&mdash;i.e., the distance from the top of rail to soffit of
+bridge&mdash;particularly as many old bridges have a very niggardly
+allowance in this respect. It may be, and quite
+commonly is, necessary to raise the rails a small amount, or,
+if headway is not restricted, to lower the soffit. Clearances
+between the running gauge and girder-work may also be
+difficult to secure, more liberal allowances being now required
+than formerly. Complications in the character of the permanent
+way, so frequently found upon old bridges, should,<span class="pagenum"><a name="Page_174" id="Page_174">[174]</a></span>
+of course, be got rid of, if possible; but the endeavour may
+introduce further difficulties. Regard must throughout be
+had to the methods to be adopted in removing old work and
+in erecting the new. Perhaps the simplest case to deal with
+is that where girders lie parallel to, and under the rails, with
+a timber floor upon which the permanent way is carried, as
+sections of the road involving pairs of girders may be readily
+removed, and replaced by the new girder-work (see <a href="#Fig93">Fig. 93</a>).
+If the deck be of trough flooring or old rails, the matter may
+not be so simple, as regard must then be had to the position
+of joints in the existing floor, and the new work be schemed
+with respect to the number and office of girders which may
+be got in at any one breaking of the road. A slight slewing
+of rails may sometimes be resorted to on occasion, where this
+has the effect of releasing some part of the work not otherwise
+to be dealt with.</p>
+
+<div class="figcenter"><a name="Fig93" id="Fig93"></a><a name="Fig94" id="Fig94"></a>
+<img src="images/illo186.png" alt="" width="450" height="325" />
+<p class="caption"><span class="smcap">Figs.</span> 93 and 94.</p>
+</div>
+
+<p>Bridges having main girders, with timber or trough flooring
+resting upon the bottom flanges, or suspended by bolts,
+will, if carrying many roads, cause some little difficulty, as
+the dismantling of any one span involves the disturbance of<span class="pagenum"><a name="Page_175" id="Page_175">[175]</a></span>
+others; where, however, many lines are concerned, it may
+be feasible to put one or more temporarily out of use, preserving
+the continuity of traffic over those which remain,
+but refraining from any diversion of the more important
+roads.</p>
+
+<p>Somewhat similar troubles occur where main girders with
+cross-girders at the lower flanges are found, particularly if
+the cross-girders are arranged in line, the ends abutting on
+each side of the same main girder webs. It is seldom, however,
+that this construction is used in bridges of small span
+carrying many roads; but where it does occur, it may necessitate
+the use of timbering below, to carry the ends of cross-girders
+when freed from their supporting main girders.
+(See <a href="#Fig94">Fig. 94</a>.)</p>
+
+<div class="figcenter"><a name="Fig95" id="Fig95"></a>
+<img src="images/illo187.png" alt="" width="500" height="109" />
+<p class="caption"><span class="smcap">Fig.</span> 95.</p>
+</div>
+
+<p>If it is proposed to use new main and cross-girders, it is
+desirable to arrange these in the manner already recommended,
+the cross-girders not in line; this has peculiar advantages in
+reconstruction work, as the bolting up and riveting of the
+cross-girder ends is not hampered by other cross-girder
+attachments, leaving each piece of floor complete in itself.
+Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence
+of one span from those adjoining (see <a href="#Fig95">Fig. 95</a>);
+but the method is wasteful of space, and involves a somewhat
+greater total weight in the main girders.</p>
+
+<p>The foregoing observations apply more generally to small<span class="pagenum"><a name="Page_176" id="Page_176">[176]</a></span>
+single-span bridges, the operations on which may be effected
+without any material disturbance of traffic arrangements;
+though this can seldom be wholly avoided, it should be confined,
+where practicable, to a few hours on a Sunday.</p>
+
+<p>The reconstruction of bridges over 70-feet span may have
+to be dealt with under more elaborate arrangements, if carrying
+two lines only, possibly with single-line working for a
+period more or less protracted; or it may be necessary, having
+regard to the weight of main girders to be removed, to carry
+the whole structure upon temporary staging, supporting the
+road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed
+erection in its ultimate position, or by erection at one side
+and drawing across. The latter method is, however, commonly
+reserved for cases in which no special staging is used
+under the old structure.</p>
+
+<p>Bridges of a number of openings are usually dealt with
+by securing full possession of one road at a time, which for
+double-line bridges necessitates single-line working. It is
+commonly out of the question, even with moderate spans,
+to deal with some of these only at a time, and so avoid continuous
+possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new
+main girders do not in any way interfere with those of the
+old, and where it is not necessary to reset bed-stones, or make
+other alterations in the bearings which necessitate the complete
+clearance of the pier-tops. In exceptional cases it may
+be found possible to arrange for the complete removal of a
+small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.</p>
+
+<p>Spans erected to one side of the final position, to be later
+travelled across, are commonly mounted upon gantry staging,
+and up to 50 tons weight may rest directly upon rails well
+greased. The power adopted to move the span is usually<span class="pagenum"><a name="Page_177" id="Page_177">[177]</a></span>
+that of screw or hydraulic jacks, or occasionally engine haulage,
+special tackle being in that case necessary to apply the
+engine power in the right direction. If the time is limited,
+or weight considerable, a more elaborate arrangement by
+which the load is supported upon wheels, may be necessary,
+with a view to reducing the resistance to a manageable
+amount. All work which it is possible to do before shifting
+into place, including the permanent way, where this is of a
+special character, should be executed in advance, leaving only
+the rail connections to be made good when the span is in
+position.</p>
+
+<p>Where timber staging is used to carry the permanent
+way before dismantling an old structure, it is convenient to
+begin by placing stout balks of timber under the sleepers
+from end to end of the bridge, or directly under the rails if
+space is limited; the staging is then arranged to give support
+to the running timbers.</p>
+
+<p>Metallic under-bridges of ample headway, perhaps over
+coal-workings (since settled down), or for some less sufficient
+reason made of metal, may be cheaply replaced by brick
+arches built below the old superstructure, the springings of
+the arch being checked into the face of the existing abutments.
+With stout walls, careful work and good material will make
+this an efficient and durable job.</p>
+
+<p>It being a primary condition of reconstruction work to
+interfere but little with ordinary traffic arrangements, single-line
+working is avoided wherever practicable; as this, always
+objectionable, may necessitate the erection of special signals
+and signal apparatus, besides the temporary remodelling of
+the roads, and in this country may involve also a Board of
+Trade inspection&mdash;altogether a troublesome and expensive
+business.</p>
+
+<p>Any bridgework which is accompanied by breaking or
+blocking the road can only be undertaken by arrangement<span class="pagenum"><a name="Page_178" id="Page_178">[178]</a></span>
+with the traffic department, after notice duly given and
+published in the periodical record of such matters; it is
+generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand
+as is possible. Wherever practicable and prudent, the
+whole work is released from its surroundings, masonry cut
+away, rivets cut out and replaced by good bolts, nuts removed
+from holding down bolts, or the bolts cut through, etc.
+Particular care should be exercised to ascertain what remains
+to be done immediately prior to removal. It is necessary
+further to arrange for trucks to be in readiness to receive old
+material, and others containing new girder work to be conveniently
+stationed, having been loaded up to come right end
+foremost; engine power, cranes, empty and loaded trucks,
+being all marshalled and so placed as to be available in proper
+order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or
+as to the reach of the crane in effecting its work.</p>
+
+<p>The whole operation to be conducted on any Sunday
+should be well within the resources of the men and plant
+engaged in it, or so managed that it is a matter of no serious
+importance if the whole cannot be completed as originally
+desired.</p>
+
+<p>Possession of the roads to be blocked having been secured
+between certain hours, if some part only of the work to be
+carried out has been completed as the time grows short, any
+attempt to execute the remainder may result in checking
+trains until such time as the line may be reported clear&mdash;a
+contingency to be avoided&mdash;though the temptation to save
+another Sunday&#8217;s work by delay of a few minutes to some
+one train may be considerable.</p>
+
+<p>In scheming any reconstruction, it may be insisted that
+at least one feasible method of carrying out the work must
+be secured, though it is the author&#8217;s experience that frequently<span class="pagenum"><a name="Page_179" id="Page_179">[179]</a></span>
+some other method than that contemplated is in the end
+adopted, when, some months later, the final arrangements
+for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered,
+with a view to a moderate amount of work being done at any
+one time, and to achieve as much more as he can himself
+secure by scheming, or a liberal use of labour; all Sunday
+work, with attendance of engines and cranes, being of necessity
+expensive.</p>
+
+<p>Railway over-bridges do not commonly present any
+particular difficulties. The spans to be dealt with are
+usually small, and the weights to be lifted moderate. The
+height above rails may, however, be above the lift of any
+crane; and, for the purpose of raising main girders, a derrick
+may become necessary, the rearing and guying of which may
+block many roads during the time it is in use. The girders
+of larger spans, too unmanageable to be lifted whole, may
+be erected upon staging; to secure the requisite headway
+it may be necessary to build the girders at a level above
+that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the
+staging.</p>
+
+<p>The widening of railway under-bridges is, as a rule, a
+matter of no special difficulty, but some remarks may be of
+use. Widenings should be planned with a regard to later
+reconstruction of the original bridge, if that is at all likely
+to be necessary, and with the object that, when complete,
+the whole should be a consistent piece of work.</p>
+
+<p>It may, indeed, happen that widening of a bridge may
+involve the remodelling or reconstruction of the old work,
+to enable the new roads to be laid down as desired; this is
+more likely to be necessary where there exist main girders
+not competent to take any additional load, and to duplicate
+which would sacrifice space between the new and old roads;<span class="pagenum"><a name="Page_180" id="Page_180">[180]</a></span>
+or it may be unavoidable because of slewing of the old rails,
+as part of a general rearrangement.</p>
+
+<div class="figcenter"><a name="Fig96" id="Fig96"></a>
+<img src="images/illo192.png" alt="" width="450" height="195" />
+<p class="caption"><span class="smcap">Fig.</span> 96.</p>
+</div>
+
+<p>Dealing with widenings simply, there is often some little
+trouble in contriving a connection between the new and the
+old work, as this may have to be made under, or close to, the
+sleeper ends of the existing roads. It is desirable to arrange
+this part so that no drilling of old work for rivets or bolts
+shall be necessary, there being, in fact, no strict connection.
+By judicious scheming, this may be effected, whilst securing
+freedom from leakage of water at the joint. (See <a href="#Fig96">Figs. 96</a>
+and <a href="#Fig97">97</a>.) If tying of the new and old structure is desired,
+this can usually be done quite simply, well below the floor at
+some more accessible level.</p>
+
+<div class="figcenter"><a name="Fig97" id="Fig97"></a><a name="Fig98" id="Fig98"></a>
+<img src="images/illo193.png" alt="" width="350" height="453" />
+<p class="caption"><span class="smcap">Figs.</span> 97 and 98.</p>
+</div>
+
+<p>The strict jointing-up of trough flooring, new to old, at
+right angles to the troughs, cannot be contemplated, but may
+be dealt with by treating each part independently, the ends
+being near together, separated by the space of an inch or so.
+Each trough end being closed up by a diaphragm or oak
+block to prevent ballast dropping through, the top of the
+space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions
+to take away leakage, as it is practically impossible to
+make this arrangement &#8220;drop dry&#8221; under the conditions
+common in executing work of this kind (see <a href="#Fig98">Fig. 98</a>).</p>
+
+<p><span class="pagenum"><a name="Page_181" id="Page_181">[181]</a></span></p>
+
+<div class="figcenter"><a name="Fig99" id="Fig99"></a><a name="Fig100" id="Fig100"></a>
+<img src="images/illo194.png" alt="" width="350" height="375" />
+<p class="caption"><span class="smcap">Figs.</span> 99 and 100.</p>
+</div>
+
+<p>Where trough flooring, new and old, has to be made good
+parallel to the troughs, the difficulty of making a direct connection
+is less marked, and it is not unusual to introduce a
+strip cover simply; but if accessible, the work is still troublesome,
+as there is commonly a want of strict alignment and
+truth as to level, between the new and the old troughs. It
+is preferable to arrange for junctions of a more convenient
+type, as in <a href="#Fig99">Figs. 99 and 100</a>.</p>
+
+<p>When widening masonry arch bridges by girder-work, it
+is desirable to insure that any girders parallel to the masonry
+face shall be sufficiently far removed from it to enable painting
+to be executed. The space remaining between the girder
+and the arch may then be bridged by floor-plates, or an extension
+of the timber floor if that is adopted.</p>
+
+<p><span class="pagenum"><a name="Page_182" id="Page_182">[182]</a></span></p>
+
+<div class="figcenter"><a name="Fig101" id="Fig101"></a><a name="Fig102" id="Fig102"></a>
+<img src="images/illo195.png" alt="" width="350" height="529" />
+<p class="caption"><span class="smcap">Figs.</span> 101 and 102.</p>
+</div>
+
+<div class="figcenter"><a name="Fig103" id="Fig103"></a>
+<img src="images/illo196.png" alt="" width="300" height="289" />
+<p class="caption"><span class="smcap">Fig.</span> 103.</p>
+</div>
+
+<p>In effecting a junction such as this, the author has used
+the arrangement shown in <a href="#Fig101">Fig. 101</a>, the advantage being
+that the piece of connecting-floor is sufficiently wide, and
+also sufficiently flexible, to allow the girder-work freedom to
+deflect without doing harm. The load carried by the width
+of floor is, as to one part, delivered well on to the old
+masonry, in preference to being imposed near to the face.
+If it should for any reason be imperative to place the girder
+close to the arch face, it is preferable to scheme the floor so
+that there shall be no actual contact, the new floor in that
+case slightly overhanging the masonry, as in <a href="#Fig102">Fig. 102</a>, or
+dealt with as in <a href="#Fig103">Fig. 103</a>, if depth is restricted.</p>
+
+<p>The widening of masonry arch bridges by masonry, calls
+for no other remark than that the new work should be free
+from the old; though it may be advisable, when the widening<span class="pagenum"><a name="Page_183" id="Page_183">[183]</a></span>
+is narrow, to tie the new work to the old in such a way as
+to permit independent settlement.</p>
+
+<p>If the widening is exceptionally narrow, there may be
+no choice but to bond the new and old work together, and
+in the best manner, with the object of minimising the risk
+of separation.</p>
+
+<p>The above matters relative to widenings, though apparently
+trifling, may by neglect cause much trouble and expense
+in maintenance. They principally concern small bridges,
+the extension of larger structures coming rather in the category
+of independent works.</p>
+
+<p><span class="pagenum"><a name="Page_184" id="Page_184">[184]</a></span></p>
+
+<h3><span class="smcap">Conclusion.</span></h3>
+
+<p>In bringing these chapters, dealing largely with questions
+affecting maintenance, to a close, it may be well to draw
+attention to the fact that economy in design (apart from
+improper reduction of sections) goes hand-in-hand with
+economy of upkeep. Given good material, that which favours
+low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to
+girders, favours also small expenditure in maintenance.
+The less complex the design, the easier will it be to keep the
+structure in order; the less the number of parts, the fewer
+will be the connections. Freedom from smithing eliminates
+liability to failure at cranks, or other work which has been
+subject to fire. It is apparent also that the free use of rolled
+instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A
+liberal depth to all girders, by reducing deflections, limits the
+inclination of the ends and gives the connections a better
+chance of remaining intact. Lastly, with work of this
+character, the labour of scraping and painting is simplified
+and cheapened.</p>
+
+<p><span class="pagenum"><a name="Page_185" id="Page_185">[185]</a></span></p>
+
+<p>The author wishes to reiterate the statement made in
+the opening paragraphs of this book, that all instances of
+decrepitude, failure, or peculiar behaviour cited, have been
+under his direct observation. The fact is insisted upon
+simply that the reader may appreciate that the information
+is at first hand.</p>
+
+<p>It has not been thought necessary, nor was it considered
+desirable, to indicate the locality of each case referred to;
+but it may be said that the matter of these chapters has been
+accumulating during many years, and relates to structures
+under the control of many different bodies.</p>
+
+<p>The study of old bridges is strongly recommended,
+particularly with respect to stress and strain, which in structures
+new or old, occur possibly as may be expected&mdash;certainly
+as they must. Consideration of existing work may thus be a
+useful check upon the fanciful requirements of some methods
+of design. There is a recent tendency, for instance, in English
+practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many
+old bridges carrying their loads with no sign of distress, should
+have failed long ago. Excess in riveting is a common extravagance,
+to which the same criticism may in a less degree
+apply. Considerable impact allowances for girders of large
+span may also be referred to as an application of empiric
+theory not justified by experience, which, as in all cases
+where such considerations fight with facts, should be modified
+or rejected.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_186" id="Page_186"></a><br /><a name="Page_187" id="Page_187">[187]</a></span></p>
+
+<h2>INDEX</h2>
+
+<ul class="index">
+<li class="first">Abutments, leaning, <a href="#Page_82">82</a>, <a href="#Page_173">173</a></li>
+<li>&mdash; movements of, <a href="#Page_158">158</a></li>
+<li>&mdash; settlement of, <a href="#Page_78">78</a></li>
+<li>Adjustment of centre girders, <a href="#Page_128">128</a></li>
+<li>&mdash; of distributing girders, <a href="#Page_120">120</a></li>
+<li>Angular distortions, <a href="#Page_88">88</a></li>
+<li>Arches, equilibrium of, <a href="#Page_162">162</a></li>
+<li>&mdash; repair of, <a href="#Page_163">163</a></li>
+<li>Arrangement of cross girders, <a href="#Page_21">21</a>, <a href="#Page_175">175</a></li>
+<li>Asphalt, <a href="#Page_26">26</a></li>
+<li class="first">Ballast, <a href="#Page_29">29</a></li>
+<li>Bearing pressure on rivets, <a href="#Page_47">47</a>, <a href="#Page_51">51</a>, <a href="#Page_57">57</a></li>
+<li>Bearings, skew, <a href="#Page_4">4</a></li>
+<li>Bottom booms, end bays, <a href="#Page_18">18</a></li>
+<li>Bracing, additional, <a href="#Page_117">117</a></li>
+<li>&mdash; effects of, <a href="#Page_34">34</a></li>
+<li>&mdash; flat bars, <a href="#Page_37">37</a></li>
+<li>&mdash; incomplete, <a href="#Page_41">41</a></li>
+<li>&mdash; sea piers, <a href="#Page_42">42</a></li>
+<li>Bridge floors, <a href="#Page_20">20</a></li>
+<li>&mdash; repairs, <a href="#Page_107">107</a></li>
+<li>&mdash; surveys, <a href="#Page_107">107</a></li>
+<li>Bridges, life of, <a href="#Page_165">165</a></li>
+<li>Breaks in <span class="lettsymb">T</span> bars, <a href="#Page_16">16</a></li>
+<li>Buckling of webs, <a href="#Page_16">16</a></li>
+<li class="first">Camber, <a href="#Page_24">24</a>, <a href="#Page_80">80</a></li>
+<li>Cast-iron arches, <a href="#Page_80">80</a>, <a href="#Page_145">145</a></li>
+<li>&mdash; &mdash; bridges, <a href="#Page_141">141</a></li>
+<li>&mdash; &mdash; columns, <a href="#Page_7">7</a>,144</li>
+<li>&mdash; &mdash; girders, <a href="#Page_141">141</a></li>
+<li>&mdash; &mdash; in sea water, <a href="#Page_101">101</a></li>
+<li>Centre girders, <a href="#Page_122">122</a></li>
+<li>Cinder ballast, <a href="#Page_29">29</a></li>
+<li>Cold-blast iron, <a href="#Page_141">141</a></li>
+<li>Cooling stresses in cast iron, <a href="#Page_145">145</a></li>
+<li>Construction depth, <a href="#Page_173">173</a></li>
+<li>Corrugated sheeting, <a href="#Page_29">29</a></li>
+<li>Cost of centre girders, <a href="#Page_135">135</a></li>
+<li>&mdash; of maintenance, <a href="#Page_168">168</a></li>
+<li>Counterbracing, <a href="#Page_19">19</a></li>
+<li>Cracked bedstones, <a href="#Page_3">3</a></li>
+<li>&mdash; columns, <a href="#Page_7">7</a></li>
+<li>&mdash; web plates, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>Cross girder arrangement, <a href="#Page_21">21</a></li>
+<li>&mdash; girders, fixed ends, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li>
+<li>&mdash; &mdash; rusted, <a href="#Page_29">29</a>, <a href="#Page_97">97</a></li>
+<li>&mdash; &mdash; weak, <a href="#Page_30">30</a>, <a href="#Page_66">66</a></li>
+<li class="first">Decay and painting, <a href="#Page_96">96</a></li>
+<li>&mdash; of floor plates, <a href="#Page_109">109</a></li>
+<li>&mdash; of timber, <a href="#Page_28">28</a>, <a href="#Page_150">150</a></li>
+<li>Deflection, <a href="#Page_85">85</a></li>
+<li>&mdash; due to booms and web, <a href="#Page_86">86</a></li>
+<li>&mdash; exceptional cases, <a href="#Page_88">88</a></li>
+<li>&mdash; in new and old work, <a href="#Page_85">85</a></li>
+<li>&mdash; working formul&aelig;, <a href="#Page_87">87</a></li>
+<li>Deformations, <a href="#Page_73">73</a></li>
+<li>Depth of girders,<span class="pagenum"><a name="Page_188" id="Page_188">[188]</a></span> <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li>
+<li>Diagonal ties, <a href="#Page_19">19</a>, <a href="#Page_42">42</a></li>
+<li>Distortion due to temperature changes, <a href="#Page_79">79</a>, <a href="#Page_84">84</a></li>
+<li>Distributing girders, <a href="#Page_120">120</a></li>
+<li>Drainage holes, <a href="#Page_25">25</a></li>
+<li>&#8220;Drop&#8221; loads, <a href="#Page_89">89</a></li>
+<li>Dwarf walls under floors, <a href="#Page_26">26</a></li>
+<li class="first">Early steel girders, <a href="#Page_68">68</a></li>
+<li>Economy, <a href="#Page_184">184</a></li>
+<li>Effect of earth slips, <a href="#Page_157">157</a></li>
+<li>&mdash; of floor on deflection, <a href="#Page_88">88</a></li>
+<li>&mdash; &mdash; &mdash; on stresses, <a href="#Page_23">23</a>, <a href="#Page_30">30</a></li>
+<li>&mdash; of high stress, <a href="#Page_86">86</a></li>
+<li>&mdash; of permanent way on stresses, <a href="#Page_18">18</a></li>
+<li>&mdash;of skew on bridge floors, <a href="#Page_25">25</a></li>
+<li>&mdash; &mdash; &mdash; on centre girders, <a href="#Page_131">131</a></li>
+<li>&mdash; of transverse bracings, <a href="#Page_34">34</a></li>
+<li>&mdash; of vibration on masonry, <a href="#Page_162">162</a></li>
+<li>&mdash; of wave action on sea piers, <a href="#Page_42">42</a></li>
+<li>End bays, bottom booms, <a href="#Page_18">18</a></li>
+<li>Equilibrium of masonry arches, <a href="#Page_162">162</a></li>
+<li>Examination of bridges, <a href="#Page_107">107</a></li>
+<li>Examples of cast-iron bridges overstressed, <a href="#Page_141">141</a></li>
+<li>&mdash; of high stress, <a href="#Page_70">70</a></li>
+<li>&mdash; of life of bridges, <a href="#Page_167">167</a></li>
+<li>&mdash; of rivet stress, <a href="#Page_56">56</a></li>
+<li>&mdash; of strengthening, <a href="#Page_114">114</a></li>
+<li>&mdash; &mdash; &mdash; by centre girders, <a href="#Page_131">131</a>, <a href="#Page_134">134</a></li>
+<li>Excessive bearing pressure, <a href="#Page_51">51</a></li>
+<li class="first">Faulty workmanship, <a href="#Page_80">80</a></li>
+<li>Fixed ends to cross girders, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li>
+<li>Flange stresses, <a href="#Page_63">63</a>, <a href="#Page_66">66</a>, <a href="#Page_67">67</a></li>
+<li>Flanges, side loaded, <a href="#Page_9">9</a>, <a href="#Page_73">73</a></li>
+<li>Flat bar bracing, <a href="#Page_37">37</a></li>
+<li>Flexing of girders, <a href="#Page_9">9</a>, <a href="#Page_74">74</a>, <a href="#Page_76">76</a></li>
+<li>Flexure curves, <a href="#Page_138">138</a></li>
+<li>Fractured bedstones, <a href="#Page_3">3</a></li>
+<li>&mdash; rails, <a href="#Page_30">30</a></li>
+<li>&mdash; webs, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>Fractures in cast iron, <a href="#Page_7">7</a>, <a href="#Page_145">145</a></li>
+<li class="first">Girder bearings, <a href="#Page_2">2</a></li>
+<li>Girders on columns, <a href="#Page_7">7</a></li>
+<li>&mdash; on masonry, <a href="#Page_8">8</a></li>
+<li>Girderwork in masonry, <a href="#Page_101">101</a></li>
+<li class="first">Headway, <a href="#Page_173">173</a></li>
+<li>High stress, <a href="#Page_61">61</a></li>
+<li>&mdash; in cast iron, <a href="#Page_141">141</a></li>
+<li>&mdash; in rivets, <a href="#Page_47">47</a>, <a href="#Page_52">52</a></li>
+<li>Holes for drainage, <a href="#Page_25">25</a></li>
+<li class="first">Impact, <a href="#Page_20">20</a>, <a href="#Page_62">62</a></li>
+<li>Inclination of girder ends, <a href="#Page_23">23</a>, <a href="#Page_53">53</a></li>
+<li>Incomplete bracing, <a href="#Page_41">41</a></li>
+<li>Initial set, <a href="#Page_88">88</a></li>
+<li>Interference with traffic, <a href="#Page_177">177</a></li>
+<li class="first">Jack arches, <a href="#Page_29">29</a>, <a href="#Page_101">101</a></li>
+<li>Joints in rails, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li>
+<li>&mdash; in trough floors, <a href="#Page_28">28</a>, <a href="#Page_180">180</a></li>
+<li>Junction between metallic and masonry bridges, <a href="#Page_183">183</a></li>
+<li>&mdash; &mdash; new and old masonry bridges, <a href="#Page_182">182</a></li>
+<li>&mdash; &mdash; new and old metallic bridges, <a href="#Page_180">180</a></li>
+<li class="first">Lattice girder stresses, <a href="#Page_47">47</a>-<a href="#Page_66">66</a></li>
+<li>Liberal depth to girders, <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li>
+<li>Life of bridges,<span class="pagenum"><a name="Page_189" id="Page_189">[189]</a></span> <a href="#Page_165">165</a></li>
+<li>Limit of elasticity, <a href="#Page_61">61</a></li>
+<li>Linen tapes, <a href="#Page_172">172</a></li>
+<li>Longitudinal floor girders, <a href="#Page_23">23</a></li>
+<li>Loose rivets, <a href="#Page_21">21</a>, <a href="#Page_25">25</a>, <a href="#Page_51">51</a>, <a href="#Page_53">53</a>, <a href="#Page_56">56</a>, <a href="#Page_109">109</a></li>
+<li class="first">Main girders, <a href="#Page_9">9</a>-<a href="#Page_17">17</a></li>
+<li>Masonry bridges, <a href="#Page_157">157</a></li>
+<li>&mdash; enduring character of, <a href="#Page_161">161</a></li>
+<li>Memel timber, <a href="#Page_150">150</a></li>
+<li>Methods of calculation, <a href="#Page_46">46</a>, <a href="#Page_61">61</a></li>
+<li>&mdash; of observing deflection, <a href="#Page_90">90</a></li>
+<li>&mdash; of setting out deflection curves, <a href="#Page_138">138</a></li>
+<li>Movements of abutments, <a href="#Page_158">158</a></li>
+<li>&mdash; of cast-iron bridge, <a href="#Page_82">82</a></li>
+<li>&mdash; of piers, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>&mdash; of rollers, <a href="#Page_7">7</a></li>
+<li>&mdash; of wrought-iron bridges, <a href="#Page_4">4</a>, <a href="#Page_21">21</a>, <a href="#Page_38">38</a>, <a href="#Page_73">73</a></li>
+<li class="first">New members to old work, <a href="#Page_116">116</a></li>
+<li class="first">Oiling steelwork, <a href="#Page_99">99</a></li>
+<li>Old drawings unreliable, <a href="#Page_108">108</a></li>
+<li>&mdash; rivets, <a href="#Page_21">21</a>, <a href="#Page_51">51</a>, <a href="#Page_54">54</a>, <a href="#Page_55">55</a></li>
+<li>Open webs, <a href="#Page_17">17</a></li>
+<li>Overhead bracing, <a href="#Page_39">39</a></li>
+<li>&mdash; girders, <a href="#Page_118">118</a></li>
+<li class="first">Painting, <a href="#Page_98">98</a></li>
+<li>Parapets, <a href="#Page_79">79</a></li>
+<li>Permissible stress in old work, <a href="#Page_110">110</a></li>
+<li>Piers, movements of, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>&mdash; out of plumb, <a href="#Page_159">159</a></li>
+<li>Piles, decay of, <a href="#Page_102">102</a>, <a href="#Page_150">150</a></li>
+<li>Pitch pine, <a href="#Page_28">28</a></li>
+<li>Plasticity, <a href="#Page_61">61</a></li>
+<li>Plate webs, <a href="#Page_9">9</a></li>
+<li>Plated floors, <a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_30">30</a></li>
+<li>Pointing masonry, <a href="#Page_164">164</a></li>
+<li>Proposed rivet stresses, <a href="#Page_58">58</a></li>
+<li class="first">Quickly applied loads, <a href="#Page_89">89</a></li>
+<li class="first">Rail joints, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li>
+<li>Rails, breaks in, <a href="#Page_30">30</a></li>
+<li>Reaction of cross girder with centre support, <a href="#Page_127">127</a></li>
+<li>Red-lead, <a href="#Page_98">98</a>, <a href="#Page_100">100</a></li>
+<li>Relative merits of bridges, <a href="#Page_169">169</a></li>
+<li>Relief by centre girders, <a href="#Page_122">122</a></li>
+<li>Repainting, <a href="#Page_100">100</a></li>
+<li>Repair of bridges, <a href="#Page_107">107</a>, <a href="#Page_147">147</a>, <a href="#Page_155">155</a>, <a href="#Page_163">163</a></li>
+<li>&mdash; of timber piles, <a href="#Page_156">156</a></li>
+<li>Replacing flange plates, <a href="#Page_110">110</a></li>
+<li>&mdash; rivets, <a href="#Page_111">111</a></li>
+<li>Resistance of cast iron to rust, <a href="#Page_101">101</a></li>
+<li>Riveted connections, <a href="#Page_45">45</a>, <a href="#Page_86">86</a></li>
+<li>Rivets in cramped positions, <a href="#Page_20">20</a></li>
+<li>&mdash; in cross girder ends, <a href="#Page_21">21</a>, <a href="#Page_49">49</a>, <a href="#Page_53">53</a>, <a href="#Page_54">54</a></li>
+<li>&mdash; in road bridges, <a href="#Page_60">60</a></li>
+<li>&mdash; in webs of main girders, <a href="#Page_46">46</a></li>
+<li>&mdash; spacing of, <a href="#Page_60">60</a>, <a href="#Page_80">80</a></li>
+<li>&mdash; stresses in, <a href="#Page_56">56</a></li>
+<li>Rocking of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>Roller bearings, <a href="#Page_7">7</a></li>
+<li>Rubble masonry, <a href="#Page_161">161</a>-<a href="#Page_164">164</a></li>
+<li>Running load and deflection, <a href="#Page_95">95</a></li>
+<li>Rusting, instances of, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li>
+<li>&mdash; of steelwork, <a href="#Page_99">99</a></li>
+<li>&mdash; over sea-water, <a href="#Page_98">98</a></li>
+<li class="first">Sag in timber bridges, <a href="#Page_150">150</a></li>
+<li>&mdash; of tapes, <a href="#Page_172">172</a></li>
+<li>Scour under piers,<span class="pagenum"><a name="Page_190" id="Page_190">[190]</a></span> <a href="#Page_161">161</a></li>
+<li>Sea piers, <a href="#Page_42">42</a>, <a href="#Page_102">102</a></li>
+<li>Setting bedstones, <a href="#Page_3">3</a>, <a href="#Page_129">129</a>, <a href="#Page_176">176</a></li>
+<li>Settlements, <a href="#Page_76">76</a>, <a href="#Page_157">157</a></li>
+<li>Skew bearings, <a href="#Page_4">4</a></li>
+<li>&mdash; bridges, right and left, <a href="#Page_173">173</a></li>
+<li>&mdash; &mdash; floors, <a href="#Page_25">25</a></li>
+<li>Skirting plate, <a href="#Page_26">26</a></li>
+<li>Slope of girder ends, <a href="#Page_92">92</a></li>
+<li>Softening of cast-iron in sea-water, <a href="#Page_101">101</a></li>
+<li>Spacing of rivets, <a href="#Page_60">60</a>, <a href="#Page_79">79</a></li>
+<li>Spread of abutments, <a href="#Page_157">157</a></li>
+<li>Spring joints, <a href="#Page_23">23</a></li>
+<li>Steel trough girders, <a href="#Page_68">68</a></li>
+<li>&mdash; troughing, <a href="#Page_70">70</a></li>
+<li>Stiffening girders from floor, <a href="#Page_12">12</a>, <a href="#Page_40">40</a></li>
+<li>&mdash; to webs, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li>
+<li>Stop piers, <a href="#Page_158">158</a></li>
+<li>Strength of light top booms, <a href="#Page_40">40</a></li>
+<li>Strengthening of bridges, <a href="#Page_107">107</a>, <a href="#Page_122">122</a></li>
+<li>&mdash; bridge floors, <a href="#Page_118">118</a></li>
+<li>&mdash; cross girders, <a href="#Page_123">123</a></li>
+<li>Stress in plated floors, <a href="#Page_31">31</a></li>
+<li>Study of old bridges, <a href="#Page_185">185</a></li>
+<li class="first">Tall piers, <a href="#Page_42">42</a>, <a href="#Page_159">159</a></li>
+<li>Timber bridges, <a href="#Page_149">149</a></li>
+<li>&mdash; floors, <a href="#Page_27">27</a></li>
+<li>&mdash; staging, <a href="#Page_177">177</a></li>
+<li>Top booms, <a href="#Page_18">18</a></li>
+<li>Traffic during reconstruction, <a href="#Page_177">177</a></li>
+<li>Transverse bracing, <a href="#Page_34">34</a>, <a href="#Page_117">117</a></li>
+<li>Trough floors, <a href="#Page_27">27</a>, <a href="#Page_180">180</a></li>
+<li>&mdash; girders, <a href="#Page_50">50</a>, <a href="#Page_74">74</a></li>
+<li><span class="lettsymb">T</span> stiffeners, breaks in, <a href="#Page_16">16</a></li>
+<li>Twin girders, <a href="#Page_15">15</a>, <a href="#Page_75">75</a></li>
+<li>Twisting of girders, <a href="#Page_11">11</a>, <a href="#Page_68">68</a>, <a href="#Page_73">73</a></li>
+<li>&mdash; &mdash; &mdash; corrected, <a href="#Page_12">12</a></li>
+<li>Types of reconstruction, <a href="#Page_174">174</a></li>
+<li class="first"><span class="lettsymb">U</span>-shaped booms, <a href="#Page_18">18</a></li>
+<li>Uncomplicated stress, <a href="#Page_62">62</a></li>
+<li>Uniform pressure on bearings, <a href="#Page_6">6</a></li>
+<li class="first">Value of E in deflection formul&aelig;, <a href="#Page_87">87</a></li>
+<li>Vibration, <a href="#Page_162">162</a></li>
+<li class="first">Wasted webs, <a href="#Page_14">14</a>, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li>
+<li>Water, scour of, <a href="#Page_161">161</a></li>
+<li>Web buckling, <a href="#Page_16">16</a></li>
+<li>&mdash; plates, cracked, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>&mdash; rivets, <a href="#Page_46">46</a>, <a href="#Page_50">50</a></li>
+<li>&mdash; stiffening, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li>
+<li>Widening masonry bridges, <a href="#Page_182">182</a></li>
+<li>&mdash; metallic bridges, <a href="#Page_179">179</a></li>
+<li>Wide spaced rivets, <a href="#Page_79">79</a></li>
+<li>Wind pressure, <a href="#Page_41">41</a>, <a href="#Page_43">43</a></li>
+<li class="first">Yielding of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+</ul>
+
+<hr class="chap" />
+
+<p class="center fsize80">LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,<br />
+GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.</p>
+
+<hr class="chap" />
+
+<div class="tnbox"><a name="TN" id="TN"></a>
+<h2>Transcriber&#8217;s Notes</h2>
+
+<p>The text of the original work (including inconsistent spelling, hyphenation, formatting etc.) has been retained, except as mentioned below.<br />
+The slight differences between the Table of Contents and the text have not been changed</p>
+
+<p><b>Changes made to the text:</b><br />
+Some punctuation errors and obvious typographical errors have been corrected silently.<br />
+Several illustrations have been moved to where they are described in the text.<br />
+Page 123, formula (2): the original shows an unclear superscript after the first L. As described in the following line of the text, this has been changed to L<sub class="lg"><i>l</i></sub>.</p>
+
+</div>
+
+<div>*** END OF THE PROJECT GUTENBERG EBOOK 44371 ***</div>
+</body>
+</html>
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+This eBook, including all associated images, markup, improvements,
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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #44371 (https://www.gutenberg.org/ebooks/44371)
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+Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Anatomy of Bridgework
+
+Author: William Henry Thorpe
+
+Release Date: December 6, 2013 [EBook #44371]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ANATOMY OF BRIDGEWORK ***
+
+
+
+
+Produced by Chris Curnow, Harry Lamé and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+
+Transcriber's Notes:
+
+Text between underscores represents _italics_, small capitals have been
+transcribed as ALL CAPITALS.
+
+Curly brackets indicate {subscripts}; letters between square brackets
+(such as [T] and [U]) represent the shape rahter than the letter itself.
+
+More Transcriber's Notes may be found at the end of this text.
+
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+  BY
+
+  WILLIAM HENRY THORPE
+  ASSOC. M. INST. C. E.
+
+  WITH 103 ILLUSTRATIONS
+
+  [Illustration]
+
+  London
+  E. & F. N. SPON, LIMITED, 57 HAYMARKET
+  New York
+  SPON & CHAMBERLAIN, 123 LIBERTY STREET
+
+  1906
+
+
+
+
+PREFACE
+
+
+In offering this little book to the reader interested in Bridgework, the
+author desires to express his acknowledgments to the proprietors of
+“Engineering,” in which journal the papers first appeared, for their
+courtesy in facilitating the production in book form.
+
+It may possibly happen that the scanning of these pages will induce
+others to observe and collect information extending our knowledge of
+this subject--information which, while familiar to maintenance engineers
+of experience, has not been so readily available as is desirable.
+
+No theory which fails to stand the test of practical working can
+maintain its claims to regard; the study of the behaviour of old work
+has, therefore, a high educational value, and tends to the occasional
+correction of views which might otherwise be complacently retained.
+
+  60 WINSHAM STREET,
+  CLAPHAM COMMON, LONDON, S.W.
+  _October_, 1906.
+
+
+
+
+CONTENTS
+
+
+  CHAPTER I.
+
+  INTRODUCTION--GIRDER BEARINGS.
+
+                                                                    PAGE
+
+  Pressure distribution--Square and skew bearings--Fixed bearings--
+  Knuckles--Rollers--Yield of supports                                 1
+
+
+  CHAPTER II.
+
+  MAIN GIRDERS.
+
+  _Plate webs_: Improper loading of flanges--Twisting of girders--
+  Remedial measures--Cracks in webs--Stiffening of webs--[T]
+  stiffeners                                                           9
+
+  _Open webs_: Common faults--Top booms--Buckling of bottom booms--
+  Counterbracing--Flat members                                        17
+
+
+  CHAPTER III.
+
+  BRIDGE FLOORS.
+
+  Liability to defects--Impact--Ends of cross and longitudinal
+  girders--Awkward riveting--Fixed ends to cross girders--Plated
+  floor--Liberal depths desirable--Type connections--Effect of “skew”
+  on floor--Water-tightness--Drainage--Timber floors--Jack arches--
+  Corrugated sheeting--Ballast--Rail joints--Effect of main girders
+  on floors                                                           20
+
+
+  CHAPTER IV.
+
+  BRACING.
+
+  Effect of bracing on girders--Influence of skew on bracing--Flat
+  bars--Overhead girders--Main girders stiffened from floor--
+  Stiffening of light girders--Incomplete bracing--Tall piers--Sea
+  piers                                                               34
+
+
+  CHAPTER V.
+
+  RIVETED CONNECTIONS.
+
+  Latitude in practice--Laboratory experiments--Care in considering
+  practical instances--Main girder web rivets--Lattice girders
+  investigated--Rivets in small girders--Faulty bridge floor--
+  Stresses in rivets--Cross girder connections--Tension in rivets--
+  Defective rivets--Loose rivets--Table of actual rivet stresses--
+  Bearing pressure--Permissible stresses--Proposed table--Immunity of
+  road bridges from loose rivets--Rivet spacing                       45
+
+
+  CHAPTER VI.
+
+  HIGH STRESS.
+
+  Elastic limit--Care in calculation--Impact--Examples of high stress
+  --Early examples of high stress in steel girders--Tabulated
+  examples--General remarks                                           61
+
+
+  CHAPTER VII.
+
+  DEFORMATIONS.
+
+  Various kinds--Flexing of girder flanges--Examples--Settlement
+  deformations--Creeping--Temperature changes--Local distortions--
+  Imperfect workmanship--Deformation of cast-iron arches              73
+
+
+  CHAPTER VIII.
+
+  DEFLECTIONS.
+
+  Differences as between new work and old--Influence of booms and web
+  structure on deflection--Yield of rivets and stiffness of
+  connections--Working formulæ--Set--Effect of floor system--
+  Deflection diagrams--Loads quickly applied--“Drop” loads--Flexible
+  girders--Measuring deflections--New method of observing deflections
+  --Effect of running load                                            85
+
+
+  CHAPTER IX.
+
+  DECAY AND PAINTING.
+
+  Examples of rusting of wrought-iron girders--Girder over sea-water
+  --Rate of rusting--Steelwork--Precautions--Red-lead--Repainting--
+  Scraping--Girders built into masonry--Cast iron--Effect of sea-
+  water on cast iron--Examples--Tabulated observations--Percentage of
+  submersion--Quality of metal                                        96
+
+
+  CHAPTER X.
+
+  EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+  Purpose--Methods of examination--Calculations--Stress in old work--
+  Methods of reducing stress--Repair--Loose rivets--Replacing wasted
+  flange plates--Adding new to old sections--Principles governing
+  additions--Example--Strengthening lattice girder bracings--Bracing
+  between girders--Strengthening floors--Distributing girders        107
+
+
+  CHAPTER XI.
+
+  STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+  Principal methods in use--Method of calculation--Adjustments--
+  Connections--Method of execution--Checks--Effect of skew on method
+  considered--Results of calculation for a typical case--Probable
+  error--Practical examples--Special case--Method of determining
+  flexure curves                                                     122
+
+
+  CHAPTER XII.
+
+  CAST-IRON BRIDGES.
+
+  Limitations of cast iron--Stress examples--Advantages and
+  disadvantages--Foundry stresses--Examples--Want of ductility of
+  cast iron--Repairs--Restricted possibilities                       141
+
+
+  CHAPTER XIII.
+
+  TIMBER BRIDGES.
+
+  Perishable nature--Causes of decay--Sag--Lateral bracing--Piles--
+  Uncertainty respecting decay--Examples--Conditions and practice
+  favourable to durability--Bracing--Protection--Repair--Piles--Cost 149
+
+
+  CHAPTER XIV.
+
+  MASONRY BRIDGES.
+
+  Definition--Cause of defects or failure--Spreading of abutments--
+  Closing in--Example--Stop piers--Example of failure--Strength of
+  rubble arch--Equilibrium of arches--Effect of vibration on masonry
+  --Safety centring--Methods of repair--Pointing--Rough dressed
+  stonework                                                          157
+
+
+  CHAPTER XV.
+
+  LIFE OF BRIDGES--RELATIVE MERITS.
+
+  Previous history--Causes of limited life--Tabulated examples of
+  short-lived metallic bridges--Timber and masonry bridges--
+  Durability--Maintenance charges--First cost--Comparative merits--
+  Choice of material                                                 165
+
+
+  CHAPTER XVI.
+
+  RECONSTRUCTION AND WIDENING OF BRIDGES.
+
+  CONCLUSION.
+
+  Measuring up--Railway under-bridges--Methods of reconstruction in
+  common use--Reconstruction of bridges of many openings--Timber
+  staging--Traffic arrangements--Sunday work--Railway over-bridges--
+  Widenings--Junction of new and old work--Concluding remarks--Study
+  of old bridgework                                                  172
+
+  INDEX                                                              187
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK.
+
+
+
+
+CHAPTER I.
+
+INTRODUCTION.
+
+
+No book has, so far as the author is aware, been written upon that
+aspect of bridgework to be treated in the following pages. No excuse
+need, therefore, be given for adding to the already large amount of
+published matter dealing with bridges. Indeed, as it too often happens
+that the designing of such constructions, and their after-maintenance,
+are in this country entirely separated, it cannot but be useful to give
+such results of the behaviour of bridges, whether new or old, as have
+come under observation.
+
+In the early days of metallic bridges there was of necessity no
+experience available to guide the engineer in his endeavour to avoid
+objectionable features in design, and he was, as a result, compelled to
+rely upon his own foresight and judgment in any attempt to anticipate
+the effects of those influences to which his work might later be
+subject. How heavily handicapped he must have been under these
+conditions is evident from the mass of information since acquired by the
+experimental study of the behaviour of metals under stress, and the
+growth of the literature of bridgework during the last forty years. That
+many mistakes were made is little occasion for surprise; rather is it a
+cause for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the study of defects
+and failures, even though they be of such a character that no
+experienced designer would now furnish like examples.
+
+Modern instances may, none the less, be found, with faults repeated,
+which should long since have disappeared from all bridgework, and are
+only to be accounted for by the unnatural divorce of design and
+maintenance already referred to. As the reader proceeds, it may appear
+that details are occasionally touched upon of a character altogether too
+crude and objectionable to need comment; but the consideration of these
+cases is none the less interesting, and, so far as the author’s
+observation goes, not altogether unnecessary.
+
+Most of the instances cited are of bridges, or parts of bridges, of
+quite small dimensions; but it is these which most commonly give
+trouble, both because the effects of impact are in such cases most
+severely felt, and possibly because the smaller class of bridges is very
+generally designed by men of less experience, than large and imposing
+structures.
+
+The particulars given relate in all cases to bridges of wrought iron,
+unless otherwise described.
+
+An endeavour has been made to secure some kind of order in dealing with
+the subject, but it has been found difficult to avoid a somewhat
+disjointed treatment, inseparable, perhaps, from the nature of the
+matter. Finally, the reader may be assured that every case quoted has
+come under the writer’s personal notice.
+
+
+GIRDER BEARINGS.
+
+In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing allowed. Clearly,
+the surface over which the pressure is distributed should be
+sufficiently ample to avoid overloading and possible crushing or
+fracture of bedstones where these exist; but if no knuckles are
+introduced, this is an extremely difficult matter to insure. A long
+bearing may deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.
+
+If the girder is made with truly level bearings, and the beds set level,
+it will certainly, when under load, throw an extreme pressure upon that
+part of the bearing surface immediately under the forward edge of the
+bearing-plate. These considerations probably account for bedstones
+frequently cracking, in addition to which possibility there is the
+disadvantage that the designer does not know where the girder will rest,
+and cannot truly define the span. The variation of flange-stress due to
+this cause may, in a girder of ordinary proportions, having bearings
+equal in length to the girder’s depth, be as much as 15 per cent. above
+or below that intended.
+
+If great care be taken in setting beds, in the first instance, to dip
+toward the centre of the span an amount depending upon the anticipated
+girder deflection, it may be possible to insure that when under full
+load the girder bearing shall rest equally upon its seat; but this is
+evidently a difficult condition to obtain practically, is good only for
+one degree of loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence of a
+slight leaning forward of abutment walls.
+
+Double or treble thicknesses of hair-felt are sometimes placed beneath
+girder bearings, with the object of securing a better distribution of
+pressure, no doubt with advantage; but this practice, though it may be
+quite satisfactory as applied to girders carrying an unchangeable load,
+hardly meets the case for loads which are variable. Notwithstanding the
+faulty nature of the plain bearing ordinarily used for girders of
+moderate span, its extreme simplicity commends it to most engineers. It
+must be admitted that no serious inconvenience need be anticipated in
+the majority of cases, particularly if the bearings are limited in
+length, do not approach nearer than 3 inches to the face of bedstones,
+and are furnished with hair-felt or similar packing.
+
+[Illustration: FIG. 1.]
+
+Whether with long or short bearings, the forward edge should be at right
+angles to the girder’s length. In skew bridges it is sometimes seen that
+this edge follows the angle of skew. The effect on the girder is to
+twist it, as will be clear from a little consideration. In evidence of
+this the case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment right up to the
+masonry face at a rather bad angle (about 15 degrees), was, after twenty
+years, found canted over at the top to the extent of 4 inches, with the
+further result of springing a joint in the top flange at about the
+middle of the girder, causing some rivets to loosen. The bedstone was
+also very badly broken at the face, and had to be replaced in the course
+of repairs (Fig. 1). This girder had, in addition to the canting from
+the upright position at its end, and the distortion of the top flange, a
+curvature in the same direction, though less in amount, at the
+bottom--an effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder end to creep
+along the abutment away from the point at which it bears hardest, under
+frequent applications and removals of the live load, and accompanying
+deflections.
+
+This tendency to travel may be aggravated in bridges carrying a
+ballasted road, in which there may be a considerable thickness of
+ballast near the bearings, by the compacting and spreading of this
+material taking effect upon the girder end, tending to push it outwards,
+being tied only by a few light cross-girders badly placed for useful
+effect. The movement may be prevented in new work for moderate angles of
+skew by carrying the end cross-girders well back, and securing them in
+some efficient manner; or by the introduction of a diagonal tie
+following the skew face, and attached to cross and main girder flanges
+(Fig. 2)--a method which may be applied to existing work also.
+
+[Illustration: FIG. 2.]
+
+For such a case as that cited it is imperative that ballast pressure at
+the girder end should be altogether eliminated.
+
+The fixing of girder ends by bolts--a practice at one time usual--hardly
+calls for remark, as it is now seldom resorted to unless for special
+reasons; but it may be well to point out the weakening effect of holes
+for any purpose in bedstones. Bed-plates commonly need no fixing; the
+weight carried keeps them in position, or if, in the case of very light
+girders upon separate plates, it is considered well to secure these from
+shifting, it may best be done by letting the plate in bodily a small
+amount, or by means of a very shallow feather sunk into a chase.
+
+[Illustration: FIG. 3.]
+
+As an improvement upon the plain bearing usually adopted, it is an easy
+matter so to design girder-ends as to deliver the load by a narrow strip
+of bearing-plate carried across the bottom flange, distributing the
+pressure upon the stone, if there be one, by means of a simple
+rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle
+will by this means result, with freedom to slide, and the girder span be
+defined within narrow limits. A true knuckle is, of course, the best
+means of securing imposition of the load always in the same place; but
+this by itself is not sufficient where the girder is of a length to make
+temperature and stress variations important, in which case rollers, or
+freedom to slide, become necessary. Bridges exist in which
+roller-bearings have been adopted without the knuckle, or its
+equivalent, but this is wholly indefensible, as it is obvious that the
+forward roller will in all probability take the whole load, and cannot
+be expected to keep its shape and roll freely under this mal-treatment.
+It is sometimes asserted that rollers are never effective after some
+years’ use; that they become clogged with dirt, and refuse to perform
+their office.
+
+There is no reason why rollers should not be boxed in to exclude dirt by
+a casing easily removed, some attention being given to them, and any
+possible accumulation of dirt removed each time the bridge is painted.
+
+To test the behaviour of rollers under somewhat unfavourable conditions
+for their proper action--that of the bearings of main roof trusses of
+crescent form, 190 feet span--the author, some thirty years since, took
+occasion to make the necessary observations, and found evidence of a
+moderate roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders resting upon
+columns, particularly if of cast iron, a roller and knuckle arrangement
+is most desirable for any but very small spans, as, if not adopted, the
+result will be a canting of the columns from side to side--a very small
+amount, it is true, but sufficient to throw the load upon the extreme
+edges of the base, though the knuckle alone will relieve the top of this
+danger. The author at one time took the trouble to examine, so far as it
+could be done superficially and without opening out the ground to make a
+complete inspection possible, a number of bridges crossing streets, in
+which girders rested upon and were secured to cast-iron columns standing
+in the line of kerb; and he found cracks, either at the top or bottom,
+in about one of every four columns.
+
+When girders passing over columns are not continuous, it may be
+difficult to find room for a double roller and knuckle arrangement; but
+this inconvenience may be overcome by carrying one girder-end wholly
+across the column-top, and securing the next girder-end to it in a
+manner which a little care and ingenuity will render satisfactory, one
+free bearing then serving to carry the load from both girders.
+
+Though the wisdom of using rollers is apparent in spans exceeding some
+moderate length, say 80 feet--as to which engineers do not seem quite
+decided--and varying with the conditions, it need not be overlooked that
+in some cases masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will yield a small
+amount without injury, and though shorter, if resting upon a bottom not
+absolutely rigid, will rock and give the necessary relief; but it is
+obvious, if the resistance to movement is sufficiently great, and the
+girder cannot slide or roll on its bearings, bedstones will probably
+loosen, as, indeed, frequently happens.
+
+
+
+
+CHAPTER II.
+
+MAIN GIRDERS; PLATE-WEBS.
+
+
+It is seldom that girders of this description--or, indeed, of any
+other--show signs of failure from mere defect of strength in the
+principal parts, even though somewhat highly stressed; and instances
+tending to support this statement will be given in a later chapter. For
+the present, it is proposed to indicate peculiarities of behaviour only,
+generally, but not always, harmless.
+
+Though now less often done, it was at one time common practice to load
+plate-girders on the bottom flange by simply resting floor timbers,
+rails, troughs, or cross-girders upon them. In outside girders one
+result of this is to cause the top flange to take a curve in plan,
+convex towards the road, every time the live load comes upon the floor
+of the bridge, upon the passing of which the flange resumes its figure,
+though still affected by that part of the load which is constant.
+
+A bridge of 47 feet span, carrying two lines of way, having one centre
+and two outside girders, with a floor consisting of old Barlow rails,
+resting upon the bottom flanges, showed the peculiarity named in a
+marked degree.
+
+The outside girders, under dead load only, were, as to the top flanges
+(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of
+straight in their length, but upon the passing of a goods engine and
+train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one
+outside girder, and 2-3/16 inches for the other.
+
+The centre girder, having a broader and heavier top flange, curved 5/8
+inch towards whichever road might be loaded. The effect of such
+horizontal flexure is clearly to induce stresses of tension and
+compression in the flanges, which, being (for the top flange) compounded
+with the normal compressive stress due to load carried, results in a
+considerable want of uniformity across the section.
+
+[Illustration: FIG. 4.]
+
+In the case under notice, the writer estimates the stresses for an outer
+girder top flange at 4·5 tons per square inch compression for simple
+loading, and 5·5 tons per square inch of tension and compression, on the
+inner and outer edges, due to flexure, resulting when compounded in a
+stress of 1 ton per square inch tension on the inside, and 10 tons per
+square inch compression on the outside edge. In this rather extreme case
+the stress on the inner edge, or that nearest the load, is reversed in
+character.
+
+The effect described appears to be not wholly due to the twisting
+moment. It is apparent that whatever curvature may be induced by
+twisting alone must be aggravated in the compression flange by its being
+put out of line.
+
+The writer does not attempt here to apportion the two effects in any
+other way than to say that the greater part of the flexure appears to be
+due to the secondary cause. Consistent with this view of the matter is
+the fact that the inclination of the girder towards the rails greatly
+exceeded the calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the floor rails
+bore hard at their extreme ends, at which point of bearing the
+calculated twisting moment accounts for less than one-half of the
+flexure observed in the flanges.
+
+[Illustration: FIG. 5.]
+
+The girders upon removal in the course of reconstruction again took the
+straight form, showing that the very frequent development of the
+stresses named had not sensibly injured the metal, though the bridge
+carried as many as three hundred trains daily in each direction, and had
+done so for very many years.
+
+The deformation of the top flange only has been noticed, yet the same
+tendency exists in the bottom, though the actual amount is much less,
+both because the lower flanges are in tension, and are also in great
+degree confined by the frictional contact of the cross bearers, even
+where no proper ties are used. In the case dealt with the bottom flanges
+of the outer girders curved 1/8 inch outwards only.
+
+With the broad flanges commonly adopted in English practice, twisting of
+the girders, under conditions similar to the above, will not generally
+be a serious matter; but with narrow flanges possessing little lateral
+stiffness it might be a source of danger.
+
+[Illustration: FIG. 6. FIG. 7.]
+
+The twisting may be limited in amount by introducing a cross-frame
+between the girders, from which they are stiffened; by strutting the
+girders immediately from the floor itself, in which case they cannot
+cant to a greater extent than that which corresponds to the floor
+deflection; or by designing the top flange to be unsymmetrical with
+reference to the web, as in Figs. 6 and 7, with the object of insuring
+that under the joint effect of vertical loading and twisting, the stress
+in the flange shall at maximum loads be uniform across the section, and
+allow it to remain straight. This may be secured by making the
+eccentricity of the flange section equal to that of the loading. For
+instance, if the load be applied 3 inches away from the web centre, the
+flange should have its centre of gravity 3 inches on the other side of
+the centre line. It can be shown that this is true throughout the length
+of the girder, and irrespective of the depth. An instance in which
+flange eccentricity being in excess, curvature outwards resulted, will
+be found in a later chapter on deformations, etc. It will not generally
+be necessary to make the bottom flange eccentric, as it is commonly tied
+in some way; but if done, the eccentricity should be on the same side as
+for the top. The flanges remaining straight under these conditions are
+not subject to the complications of stress referred to in the case first
+quoted. The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the kind
+discussed.
+
+It should be remarked that by the two first methods, if the stiffening
+frames are wide apart and attached direct to the web, there is a
+liability for this to tear, under distress, rather than keep the girder
+in line.
+
+There is one other possible consequence of throwing load upon the
+flanges of a girder of a much more alarming nature. In girders not very
+well stiffened, it may happen that the frequent application of load in
+this manner finally so injures the web-plate, just above the top edge of
+the bottom angle-bars, as to cause it to rip in a horizontal direction.
+More likely is this to happen with a centre girder taking load first on
+one side, then on the other, and again on both together. Cases may be
+cited in which cracks right through the webs 3 feet or more in length
+have resulted from this cause. It is very probable, however, that in
+some of these cases the matter was aggravated by the use of a poor iron
+in the webs, as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a girder, would,
+if they could not be made thin enough, even encourage the use of an
+indifferent metal as being quite good enough for that part of the work.
+
+An instance of web-fracture from somewhat similar causes may be here
+given.
+
+In a bridge of 31 feet 6 inches effective span, and consisting of twin
+girders carrying rails between, as shown in Figs. 8 and 9, the load
+resting upon the inner ledges, formed by the bottom flange, induced
+such a bending and tearing action along the web just above the
+angle-bars, as to cause a rip in one of the girders, well open for some
+distance, and which could be traced for 14 feet as a continuous crack.
+
+[Illustration: FIG. 8.]
+
+[Illustration: FIG. 9.]
+
+It will be noticed in the figure that the [T] stiffeners occur only at
+the outer face of the web, and that the inner vertical strips stop short
+at the top edge of the angles, the result being that under load the
+flange would tend to twist around some point, say A, at each stiffener,
+inducing a serious stress in the thin web at that place, while away from
+these stiffeners the web would be more free to yield without tearing.
+The fact that at a number of the stiffeners incipient cracks were
+observed, some only a few inches long, suggests this view of the matter.
+
+A case of web-failure from other influences coming under notice showed
+breaks at the upper part of the web extending downwards.
+
+In this bridge, of 32 feet span, which had been in existence thirty-two
+years, the webs--originally 1/4 inch thick--were, largely because of
+cinder ballast in contact with them, so badly wasted as to be generally
+little thicker than a crown-piece, and in places were eaten through; in
+addition to which, the road being on a sharp curve, the rail-balks had
+been strutted from the webs to keep them in position, the effect of
+which would be to exert a hammering thrust upon the face of the web at
+the abutting ends, and assist in starting cracks in webs already much
+corroded. A feature of this case, tending to show that the breaks
+resulted as the joint effect of waste and ill-usage by the strut
+members, rather than by excessive stress in the web as reduced, is to be
+found in the fact that the girders when removed were observed to be in
+remarkably good shape--i.e. the camber, marked on the original drawings
+to be 1-1/2 inch, still showed as a perfectly even curve of that rise,
+which would hardly have been the case if the lower flange had been let
+down by web-rupture, the result of excessive web-stresses.
+
+Occasionally webs will crack through the solid unwasted plate, in a line
+nearly vertical; not where shear stress is greatest, but generally at
+some other place, and from no apparent cause, either of stress or
+ill-usage. The writer has observed this only in the case of small
+girders not exceeding 2 feet in depth; and, for want of any better
+reason, attributes these cracks to poor material, coupled with some
+latent defect. In a bridge having some thirty cross-girders, each 26
+feet long, about every other one had a web cracked in this manner after
+many years’ use.
+
+Web-cracks of the kind first indicated, are perhaps, the most probable
+source of danger in plate-girders, of any which are likely to occur. The
+fault is insidious, difficult to detect when first developed, and
+perhaps not seen at all till the bridge, condemned for some other
+reason, has the girders freely exposed and brought into broad light. The
+manner in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of these defects
+an uncertain matter, unless sufficient trouble is occasionally taken to
+render inspection complete.
+
+The manner in which girders with wasted and fractured webs will still
+hang together under heavy loading seems to warrant the deduction that,
+in designing new work, it can hardly be necessary to provide such a
+considerable amount of web-stiffening as is sometimes seen; experience
+showing that defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form of
+cracks.
+
+A case of web-buckling lies, so far, without the author’s experience.
+There is no need to introduce, for web-stresses alone, more stiffening
+than that which corresponds to making the stiffeners do duty as vertical
+struts in an openwork girder; in which case it is sufficient to insure
+that the stiffeners occurring in a length equal to the girder’s depth
+shall, as struts, be strong enough in the aggregate to take the whole
+shear force at the section considered, in no case exceeding this amount
+on one stiffener. For thin webs in which the free breadth is greater
+than one hundred and twenty times the thickness, the diagonal
+compressive stress may be completely ignored, and the thickness
+determined with reference to the diagonal tension stress only.
+
+There is one fault which frequently shows itself in stiffeners though
+not the result of web-stresses, and when performing an additional
+function--viz., the breaking of [T] stiffener knees at the weld, where
+brought down on to the tops of cross-girders, due to the deflection of
+the floor, as shown in Fig. 10. When such knees are used, the angle may
+properly be filled in with a gusset-plate to relieve the weld of strain
+and prevent fracture.
+
+[Illustration: FIG. 10.]
+
+There is some little temptation in practice to make use of the solid web
+as a convenient stop for ballast, or road material. Special means,
+perhaps at the cost of some little trouble, should be adopted, where
+necessary, to avoid this.
+
+
+MAIN GIRDERS; OPEN WEBS.
+
+With these, as with plate-girders, deficiency of strength--i.e. of
+section strength--is seldom so marked as to be a reasonable cause of
+anxiety. In particular instances faults in design may result in stresses
+of an abnormal amount, though rarely to an extent occasioning any ill
+effects. The practice of loading the bottom flanges at a distance from
+the centre, the bad effects of which have already been dealt with as
+applied to plate-girders, is not commonly resorted to in girders having
+open webs, nor are these so liable to be heaped with ballast in
+immediate proximity to essential members of the structure.
+
+Some defects are, however, occasionally seen which may be remarked. Top
+booms of an inverted [U] section are sometimes made with side webs too
+thin, and having the lower edges stiffened insufficiently, or not at
+all. Where this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to sustain the
+compressive stress to which the rest of the boom is liable. The practice
+of putting the greater part of the boom section in an outer flange,
+characteristic of this defect, has the further disadvantage of throwing
+the centre of gravity of the section so near its outer edge as to make
+impracticable the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section is thrown into
+the flange-plates, the centre of gravity of the section has no constant
+position along the boom--an additional inconvenience where correct
+design is aimed at.
+
+These considerations indicate the propriety of arranging the bulk, or
+all, of the section at the sides, thus reducing or getting rid of the
+objections named.
+
+Where the bottom boom consists of side plates, only one point demands
+attention. It is found that, though nominally in tension, the end bays
+are liable occasionally to buckle, as though under compressive stress,
+and need stiffening, not excepting girders which at one end are mounted
+on rollers. This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes, such as
+wind forces, or as in the case of a bridge carrying a railway, in which
+the rigidity of the permanent-way may be such that the bridge-structure,
+in extending towards the roller end, cannot move it sufficiently,
+causing a reversal of stress on the lighter portions of the bottom boom
+at the knuckle end; or by the exposed girder booms becoming very
+sensibly hotter than the bridge floor, and by expanding at a greater
+rate, cause this effect, from which rollers cannot protect them.
+
+In counterbracing consisting of flat bars it is desirable either to
+secure these where they cross other members, or stiffen them in some
+manner to avoid the disagreeable chattering which will otherwise
+commonly be found to occur on the passage of the live load.
+
+Occasionally diagonal ties are made up of two flat bars placed face to
+face, to escape the use of one very thick member. Where this is done,
+the two thicknesses, if not riveted together along the edges, will be
+liable to open, as the result of rusting between the bars in contact,
+when the evil will be aggravated by the greater freedom with which
+moisture will enter the space.
+
+Other matters relating to open-web girders will be more conveniently
+dealt with under their separate headings, particularly a further
+consideration of the relationship subsisting between the booms and floor
+structure.
+
+
+
+
+CHAPTER III.
+
+BRIDGE FLOORS.
+
+
+The floors of bridges commonly give more trouble in maintenance, and
+their defects are more frequently the cause which renders reconstruction
+necessary, apart from reasons not concerning strength, than any other
+part of such structures. When it is considered that this portion of a
+bridge is first affected by impact of the load which comes upon it, and
+is usually light in comparison with the main girders further removed
+from the load, and to which the latter is transferred through the more
+or less elastic floor, the fact will be readily appreciated by those not
+already familiar with it.
+
+The end attachments of cross and longitudinal girders are very liable to
+suffer by loosening of rivets, or, more rarely, by breaking of the
+angle-irons which commonly make such a connection. A not unusual defect
+of old work, which may also sometimes be seen in work quite new, where
+the cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends. There is
+small chance of these ever being properly tight, if the act of riveting
+is rendered difficult by bad design. This is the more objectionable if
+it happens that cross-girder ends abut against opposite sides of the web
+of an intermediate main girder, and are secured by the same rivets
+passing through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which they become
+subject, as the cross-girders take their load and deflect under it,
+will be very apt to loosen them. The author has seen a case of this kind
+(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the
+whole of the cross-girder end rivets were loose, some nearly worn
+through, thus allowing the cross-girders to be carried, not by their
+attachments, but by resting upon the main-girder flanges, which in turn,
+by repeated twisting, tore the web for a length of 4 feet; there was
+also pronounced side flexure of the top booms. The movements generally
+on this bridge (of 42-feet span), whether of main or cross-girders, were
+very considerable and disturbing. It was removed after about
+twenty-three years’ use.
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+There is no necessity, as a rule, for the ends of cross-girders attached
+to the same main girder at opposite sides to be placed in line. The
+author prefers to arrange them to miss, by which device each connection
+is entirely separate, the riveting can be more efficiently executed,
+erection is simplified, and the rivets will be more likely to keep
+tight. Other special cases of cross-girder ends will be dealt with under
+the head “Riveted Connections.”
+
+It is sometimes contended that cross-girders attached at their ends by a
+riveted connection should be designed as for fixed ends, in which case
+they are usually made of the same flange section throughout, with a view
+to satisfy the supposed requirements. But a girder to be rightly
+considered as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction, and no
+overhead bracing, this is so far from being the case as to leave little
+occasion for taking the precaution named. As the cross-girders deflect,
+the main girders will commonly yield slightly, inclining bodily towards
+the cross-girders, if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in this manner is
+usually less than that which corresponds to fixing the cross-girder
+ends, and is, generally, slight. It is, of course, necessary that this
+measure of resistance at the connection should be borne in mind for the
+sake of the joint itself, quite apart from any question of fixing.
+
+Possibly, in quite exceptional cases, where very stiff main girders are
+braced in such a manner as to prevent canting, it may be proper to
+consider the cross-girder ends as fixed, or for those near the bearings
+of heavy main girders; but the author has not met with any example where
+cross-girders, apart from attachments, appear to have suffered from
+neglect of this consideration.
+
+With cross-girders placed on either side of a main girder, and in line,
+it may also, for new work, be desirable to regard the ends as fixed, and
+to detail them with this in view. It does not, however, appear wise to
+carry this assumption to its logical issue, and reduce the flange
+section to any appreciable extent on this account. The fixity of the
+ends will, in any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a moderate effect in
+reducing flange stress at the middle of the loaded floor beam.
+
+[Illustration: FIG. 13. FIG. 14. FIG. 15.]
+
+Similar reasons affect the design of longitudinal girder attachments to
+cross-girders, which, if intended to support rails, cannot of necessity
+be schemed to come other than in line. Where the floor is plated as one
+plane surface, there will not usually be any trouble resulting if no
+special precautions are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving the
+joints of abnormal stress. If the plating is, however, designed in a
+manner which does not present this advantage, or if the floor be of
+timber, it is better to decide whether the connections shall be
+considered as fixed, and made so; or avowedly flexible, and detailed in
+such a manner as to possess a capacity for yielding slightly without
+injury. Those connections are most likely to suffer which are neither of
+the one character nor the other, offering resistance without the ability
+to maintain it. Figs. 13, 14, and 15 give representations of three
+“spring joint” methods of insuring yield in a greater or less degree.
+For small longitudinals it is, perhaps, sufficient to use end angles
+with very broad flanges against the cross-girder web; these to be
+riveted in the manner indicated in Fig. 15.
+
+Liberal depth to floor beams is distinctly advantageous where it can be
+secured, rendering it easier to design the ends in a suitable manner, by
+giving room near mid-depth of the attachment to get in the necessary
+number of rivets; or where the ends are rigidly attached direct to
+vertical members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with a
+correspondingly reduced cant of the main girders and flexure of the
+vertical member, with smaller consequent secondary stresses. In any case
+deep girders will contribute to stiffness of the floor itself,
+favourable in railway bridges to the maintenance of permanent-way in
+good order.
+
+[Illustration: FIGS. 16, 17, 18.]
+
+A point in connection with skew-bridge floors occasionally overlooked is
+the combined effect of the skew, and main girder camber, in throwing the
+floor structure out of truth, if no regard has been paid to this. The
+result is bad cross-girder or other connections; or, in the case of
+bearers running over the tops of main girders, a necessity for special
+packings to bring all fair (Fig. 17). The author has in such cases,
+where cross-girders are used, set the main girder beds at suitable
+levels, in order that the cross-bearers may all be horizontal (see Figs.
+16 and 18). This may not always be permissible; but, however the
+difficulty may be met, it should be dealt with as part of the design.
+For small angles of skew only may it be neglected.
+
+Rivets attaching cross-girder angles to the web will occasionally
+loosen, probably due in most cases to bad work, together with some
+circumstance of aggravation, as in the case of a bridge floor consisting
+of girders spaced 3 feet 6 inches apart, with short timber bearers
+between, carrying rails. In many girders the top row of rivets, of
+ordinary pitch and size, had loosened, allowing the web, about 1/4 inch
+thick, a movement of 1/8 inch vertically. The rails being very close
+down upon the cross-girder tops, though not intended to touch, had at
+some time probably done so, and by “hammering” produced the result
+described.
+
+Plated floors are often found which are objectionable on account of
+their inability to hold water, arising sometimes from bad work, as often
+from wide spacing of rivets. With rivets arranged to be easily got at,
+and pitched not more than 3 inches apart, a tight floor may be expected;
+but it is still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside of the
+plate, and sufficiently long to deliver direct into gutters, where these
+are necessary. Drain-holes should not be less frequent than one to every
+50 square feet of floor, if flat, and may advantageously be more so.
+Gutters should slope well, and care be taken to insure practicable
+joints and good methods of attachment--a matter too often left to take
+care of itself, with considerable after-annoyance as a result.
+
+The use of asphalt, or asphalt concrete, to render a plated floor
+water-tight is hardly to be relied upon for railway bridges, though no
+doubt effective for those carrying roads. It is extremely difficult to
+insure that it shall stand the jarring and disturbance to which it may
+be subject, and under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying of the floor.
+In bulk, as in troughs, it may be useful, but in thin coverings on
+plates it cannot be depended upon.
+
+Floors having plated tops are sometimes finished over abutments or piers
+in a manner which is not satisfactory, either as regards the carrying of
+loads or accessibility for painting. If the plates are carried on to a
+dwarf wall with the intention that the free margin of the plate shall
+rest upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after the girder work
+is in place, making it difficult to insure that the wall really supports
+the plate, the result being that this may have to carry itself as best
+it can. In any case, severe corrosion will occur on the underside, and
+the plate rust through much before the rest of the floor; the masonry
+also will usually be disturbed.
+
+It appears preferable to form the end of the floor with a vertical
+skirting-plate having an angle or angles along the lower edge. This may
+come down to a dwarf wall, but preferably not to touch it, the skirting
+being designed to act as a carrying girder. A convenient arrangement is
+shown in Fig. 19, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the skirting
+referred to being carried continuously along the floor edge, and
+attached to each girder-web, the whole of the more important parts being
+open to the painter.
+
+[Illustration: FIG. 19.]
+
+Trough floors consisting of one or other of the forms of pressed or
+rolled section present the objection that it is almost impracticable to
+arrange an efficient connection at the ends, if they abut against main
+girders, and but little connection is, as a rule, attempted, and
+sometimes none. The result is that the load from these troughs is
+delivered in an objectionable manner, and the ends being open or
+imperfectly closed, water and dirt escape on to the flange, or other
+ledge, which supports them. A description of pressed floor which
+promises to overcome this objection, and provide a ready means of
+attachment to the webs of plate-girders, or of booms having vertical
+plate-webs, has within the last few years been introduced. This has the
+ends shaped in such a manner as to close them and provide a flat surface
+of sufficient area for connection by rivets. Each hollow is separately
+drained by holes with nozzles. Whether this type of trough will develop
+faults of its own, due to over-straining of the metal in the act of
+pressing, remains to be seen; but as it appears possible to produce the
+desired form without any material thinning or thickening of the metal,
+the contention that no severe usage accompanies the process appears to
+be reasonable.
+
+That form of troughing in which the top and bottom portions are
+separately formed, and connected by a horizontal seam of rivets at
+mid-depth, is found in use upon railway bridges to be very liable to
+loosening of those rivets near the ends; less surprising, perhaps,
+because the sloping sides are usually thin.
+
+It is a distinctly difficult matter to join two or more lengths of any
+trough flooring having sloping sides, in a workmanlike manner; the fit
+of covers is apt to be imperfect, and some rivets, being difficult of
+access, are likely to be but indifferently tight, so that if the joint
+occurs where it will be more than lightly stressed, trouble will
+probably follow. A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most severe, any
+leakage come directly upon the girder, and remedial measures be more
+difficult to carry out.
+
+Timber floors of the best timber, close jointed, are more durable than
+might be supposed. The disadvantage is a difficulty in ascertaining the
+precise condition of the timber after many years’ use. The author has
+seen timbers, 9 inches by 9 inches, forming in one length a close floor,
+carried by three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces with the
+foot; whilst in another case, with the same arrangement of girders and
+close-timbered floor, the wood, after being in place for thirty-two
+years, was, when taken out, found to be perfectly sound, with the
+exception of a very few bad places of no great extent. In this instance,
+however, it is known that the floor--pitch-pine--was put in by a
+contractor who prided himself upon the quality of the timber that he
+used; the floor being also covered with tar concrete, which had in this
+instance so well performed its office as to keep the timber quite dry on
+the top.
+
+Jack arches between girders make an excellent floor for road bridges,
+though heavy; and for small bridges may be used to carry rails, if the
+girders are designed to be stiff under load. The apprehension that
+brickwork or concrete will separate from the girder-work, or become
+broken up under even moderate vibration, does not seem to be well
+founded, if the deflection is small and the brickwork or concrete good.
+
+The use of corrugated sheeting as a means of rendering the underside of
+a bridge drop dry cannot be too strongly deprecated. If it must be
+adopted, the arrangement should be such as to permit ready removal for
+inspection and painting. It is evident that by boxing up the floor
+structure, rust is favoured, and serious defects may be developed, not
+to be discovered till the sheeting is removed, or something happens.
+
+[Illustration: FIG. 20.]
+
+A case may be instanced in which it was found, on taking down sheeting
+of this description, that the floor girders, previously hidden, were
+badly wasted in the webs. One of these girders had cracked, as shown in
+Fig. 20, and others were in a condition only less bad.
+
+In any floor carrying ballast or macadam, if means are not adopted to
+keep the road material from the structure of the floor, or from the main
+girders, corrosion may be serious in its effects. Cinder ballast is,
+perhaps, the worst in this respect, in its action upon steel or
+ironwork, being distinctly more damaging than any other kind commonly
+used.
+
+Rail-joints upon bridge floors are to be avoided where practicable by
+the use of rails as long as can be obtained; if the bridge is small
+enough, crossing it in one length. At each joint there is likely to be
+hammering and working extremely detrimental to floor members and
+connections; indeed, it may happen that loose rivets will be found in
+the neighbourhood of such joints, and nowhere else on the bridge. Where
+rail-joints cannot be avoided, their position should, if there be any
+choice, be judiciously selected, and the plate-layers taught to close
+the joints and jam the fish-bolts.
+
+[Illustration: FIG. 21.]
+
+As rail-joints upon a bridge may injuriously affect the floor, so also
+will a weak floor be very trying to the rails. A remarkable instance of
+this has come under the writer’s notice, where a bridge (Fig. 21) of
+three 33-feet spans, having outer and centre main girders, with
+cross-girders spaced 3 feet apart, resting upon the girder flanges, but
+not attached, and carrying two roads, had the permanent-way in a very
+bad state. The rails proper, with supplementary angle-plates, rested
+direct upon the cross-girders, which were decidedly light, and the whole
+floor had much “life” in it, the ill-effect of which was shown in
+thirteen breaks in the angle-plates, in each case near their ends,
+generally at holes.
+
+It appears probable that severe stresses may be thrown upon the parts of
+a floor, whether placed at the level of the bottom booms or of the top,
+by changes of length in the booms due to stress. The author has,
+unfortunately, no direct evidence to offer in reference to this, tending
+either for or against the contention. If an unplated floor of cross and
+longitudinal girders of usual arrangement be at the bottom boom of a
+large bridge, as the boom lengthens with the imposition of load upon the
+bridge, all the cross-girders from the centre towards the abutments will
+be curved horizontally, the middle portion being restrained by the
+longitudinals from moving bodily with the ends. Each cross-girder except
+that at the centre, if there be one, will thus present a figure in plan,
+concave towards the abutment to which it is nearest. This will be
+accompanied by stressing of the connections, and a transfer to the
+longitudinals of as much of the tensile stress properly belonging to the
+booms as the stiffness of the cross-girders may communicate.
+
+This in itself will hardly be considerable, and will be the less on
+account of a slight yielding which may be expected at the end
+connections of each longitudinal; but the effect upon the cross-girders
+by horizontal bending will be much marked. If the case be supposed of a
+200-feet span in steel at ordinary loads and stresses, carrying one line
+of way, with cross-girders 20 feet apart, and having no floor-plates, it
+may be ascertained, neglecting for the moment any slight yielding of the
+longitudinal girder connections, that upon the bridge taking its full
+live load there will be the following approximate results: Movement at
+each end of the end cross-girders of 3/10 inch, equivalent to a force of
+7-1/2 tons, tending to bend them horizontally, and a mean stress on the
+outer edges of the girders, 12 inches wide, of 8 tons per square inch
+due to flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge, of
+3/4 ton per square inch. Normal elongation of the longitudinal girder
+bottom flanges, and compression of the top, modifies the figures
+unfavourably as to the cross-girder top flange. Yielding of the
+connections named before has been neglected in arriving at these
+stresses. If they are sufficiently accommodating to give freely, to a
+mean extent, as between the top and bottom of each joint, of 1/29 inch,
+these results will disappear. It is evident, however, that we cannot
+rely upon good work yielding without the existence of considerable
+forces to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.
+
+The most favourable case has been taken; if now it is assumed that the
+floor has continuous plating, the results would seem to be much more
+astonishing. It will appear on this supposition that the boom stresses,
+instead of being taken wholly by the booms, are about equally divided
+between these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which for the end
+cross-girders will approach 40 tons at each connection--considerably
+more than the vertical reaction under normal loads.
+
+Palpably, these conclusions must be greatly modified by the yield of
+longitudinal girder ends, and slip of the floor rivets in transverse
+seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the
+stress at each, as estimated, would be sufficient to induce shear of
+about 6 tons per square inch--more than enough to cause “slip.” After
+making this allowance, it is still evident there must be very serious
+forces at work about the ends of cross-girders under the conditions
+supposed, probably not less than one half the amounts named, as with
+this reduction the floor rivets should not yield, given reasonably good
+work. It is to be observed that the effect of live load only has been
+introduced, on the presumption that the longitudinals and floor-plating
+have not been riveted up till the main girders have been allowed to
+carry the major part of the dead load; but even this cannot always be
+conceded. The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these possible
+effects, either with the object of rendering the communication of these
+forces harmless, or making the floor so that it shall take little or no
+stress from the main booms, by arranging joints across the floor
+specially designed to yield, the ends of longitudinals being schemed
+with the same object. Where there is no plating, the case is, perhaps,
+sufficiently provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these girders
+upon the top of the cross-girders, when stretching of the bottom flanges
+of the rail-bearers under load may be expected, within a little, to keep
+pace with the lengthening of the main booms.
+
+It would appear that light pressed troughs running across the
+longitudinals would, by yielding in every section, also furnish relief,
+as compared with the rigidity of flat plates.
+
+By placing the floor at a level corresponding to the neutral axis of the
+main girders, the communication of stress to the floor may be avoided;
+but it seldom happens that there is so free a choice as to floor height
+relative to the girders. This solution is, therefore, of limited
+application.
+
+It is obvious that somewhat similar effects must obtain to those
+considered in detail, when the floor structure lies at the level of top
+booms, but with forces of compression from the booms to deal with,
+instead of tension.
+
+
+
+
+CHAPTER IV.
+
+BRACING.
+
+
+Bracing, whether to strengthen a structure against wind, to insure the
+relative positions of its parts, or for any other purpose, cannot be
+arranged with too great care and regard to its possible effects. Forces
+may be induced which the connections will not stand, with loose rivets
+as a consequence, and inefficiency of the bracing itself; or, the
+connections holding good, stresses in the main structure may, perhaps,
+be injuriously altered.
+
+To take a not uncommon case, let us suppose a bridge consisting of four
+main girders placed immediately under rails of ordinary gauge, and
+braced in vertical planes only, right across from one outer girder to
+the other. If the roads were loaded always at the same time, nothing
+objectionable would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and deflects, the bracing
+under the six-foot will endeavour to communicate some part of this load
+to the other pair of girders. If the bracing is so designed that some
+correctly calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections, there
+will be no harmful consequences; but if not, the bracings will most
+probably work at the ends; this, indeed, is what frequently happens.
+There is one other effect which will ensue, if the bracing is wholly
+efficient; a certain twisting movement of the bridge will occur, which
+increases the live load upon the outer girder on the loaded side of the
+bridge to the extent of 10 per cent., with a corresponding lifting force
+at the outer girder on the unloaded side. These amounts are not serious,
+but wholly dispose of any advantage it is conceived will be gained by
+causing the otherwise idle girders to act through the medium of the
+bracing. In road bridges of similar arrangement, over which heavy loads
+may pass on any part of the surface, it is clear that the use of bracing
+between girders should not be taken as justifying the assumption that
+the load is distributed over many girders, and correspondingly light
+sections adopted, unless the effect of twisting on the whole bridge is
+also considered, and justifies this view; for, as already stated in the
+case of the railway bridge, the net result may be to increase the girder
+stresses instead of reducing them. Generally, it may be deduced that the
+better plan for railway bridges is to brace the girders in pairs,
+leaving, in the case supposed, no bracing between the two middle
+girders, though there will be no objection to connecting these by simple
+transverse members of no great stiffness, to assist in checking lateral
+vibration. For road bridges of more than five longitudinal girders,
+equally spaced, it may be advantageous to brace right across, the
+twisting effect with this, or a greater, number of girders not, as a
+rule, leading to any increase of load on any girder. Figs. 22 to 25 give
+the distribution of live load, placed as shown, for 3, 4, 5, and 6
+girders.
+
+It is to be observed that these statements do not apply to cases where
+there may be also a complete system of horizontal bracing, the effect of
+which, in conjunction with cross diagonals, may be greatly different,
+with considerable forces set up in the bracing, and a modification of
+girder stresses.
+
+These effects may be so considerable as to call for special attention in
+design where such an arrangement is adopted.
+
+[Illustration: FIG. 22.]
+
+[Illustration: FIG. 24.]
+
+[Illustration: FIG. 23.]
+
+[Illustration: FIG. 25.]
+
+Somewhat similar straining to that first indicated may occur in bracings
+placed between the girders of a bridge much on the skew. If this is, on
+plan, at right angles to the girders, as is commonly and properly the
+case, the ends will evidently be attached to the girders at points on
+their length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts, and the
+bracing will, if at one end attached near a rigid bearing, transfer some
+part of the load from one girder to the other, notwithstanding that
+both girders may be of the same span and equal extraneous loading. It
+would not be difficult to ascertain the amount of load so transferred
+from a consideration of the relative movements if free, and the loads on
+the two girders necessary to render these movements equal, if the
+deflections were simply vertical; but as there will be some twisting and
+yielding of the girders on their seats, the calculation becomes
+involved. If the bracing is placed at about the middle of the girders,
+the effects noted will be greatly reduced; first, because the difference
+of movements near the centre will be less; second, any given difference
+will correspond to a smaller transference of load; and, third, because
+each girder will there be more free to twist than at the ends. It
+therefore appears that bracings between the girders of a skew bridge
+should not be placed near the bearings, though they may be put, with
+much less risk of injury, near the middle.
+
+Cross-girders on a skew bridge are subject to forces somewhat similar to
+those which may affect bracing, rendering it desirable to design their
+attachments in a manner which shall not aggravate the matter, but rather
+reduce the effects of unequal vertical displacement of their ends where
+secured to the main girders.
+
+Crossed flat bars as bracing members are objectionable on account of
+their tendency to rattle, after working loose; but as this effect only
+ensues in bracing which has first become loose (it being assumed that
+the bars in any case are connected where they cross), this objection is
+not itself vital, though greater rigidity is easily obtained by making
+all such members of a stiff section.
+
+Defective bracing between girders, from neglect of the very considerable
+forces it may be called upon to communicate, is very common; the writer
+has seen many such cases, of which one is here illustrated in Fig. 26.
+
+[Illustration: FIG. 26.]
+
+This bridge, of the section shown, and 85 feet span, had very light web
+structure. The bracings, of which there were two sets, were wholly
+inefficient, the end rivets being loose in enlarged holes. Upon the
+passage of a train there was a positive lurching of the girder tops from
+side to side. The integrity of the bridge was really dependent upon
+such stiffness as there was in the girders, and unplated floor.
+
+A common but indifferent method of keeping the top members of main
+girders in line is by the use of overhead girders alone, frequently
+curved to give the requisite clearance over the road. This cannot be
+considered as wholly inefficient, as sometimes maintained, since it is
+evident that the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must take a greater
+force to distort it than would be necessary to cause deformation of a
+corresponding degree, in an open frame formed by the omission of the
+overhead girder; but it is not a method to be recommended, its precise
+utility is difficult to estimate, and, if the cross-girder attachments
+are of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however, not applicable
+to this arrangement alone. All overhead bracing favours this by
+restraining the tendency of the top booms to cant inwards when the floor
+beams are loaded; and though this restraint may be quite harmless, it is
+desirable that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in its character.
+“Sway” bracing, sometimes introduced at right angles to the bridge
+between opposite verticals, tends to emphasise these effects by
+rendering the cross-section of the bridge still stiffer, besides making
+it a matter of difficulty to ascertain how much of the wind forces on
+the top boom is carried to the abutment by the top system of bracing,
+and how much by the floor. The author does not, however, mean to suggest
+that it cannot be used with propriety, but rather that extreme care is
+desirable in considering its ultimate effect on the rest of the
+structure.
+
+For girders of moderate depth there may be on these grounds a distinct
+advantage in abandoning overhead bracing, and securing rigidity of the
+top boom, and adequate resistance to wind forces, by making the
+connection between the cross-girders and the web members sufficiently
+good to insure, as a whole, a stiff [U]-shaped frame; but this, with the
+ordinary type of rocker arrangement under the main girder bearings, will
+not be entirely free from objection, as canting of the girders due to
+floor loading will throw extreme pressure on the inner end of each
+rocker. There appears to be no reason why the cylindrical knuckle should
+not in this case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.
+
+[Illustration: FIG. 27.]
+
+The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom flanges,
+renders very narrow top booms permissible. This is a decided advantage
+where lightness of appearance is aimed at; but it is not unusual to see
+an attempt made in this direction by introducing gusset plates of very
+ample proportions between vertical members of the girders, and the
+projecting ends of flimsy transoms, carried beyond the width of the
+bridge proper, these being of a section wholly out of proportion to the
+brackets they are supposed to secure. Whatever may be the amount of
+strength necessary at the point A, in Fig. 27, there should not be less
+throughout the transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the vertical
+stiffeners is not, as a rule, great. Information to enable this question
+to be dealt with as a matter of calculation is somewhat scanty; but it
+would appear to be sufficient to insure safety that, for an assumed
+small amount of curvature in the compression member, the forces outwards
+corresponding to this curvature, due to thrust, should be resisted by
+verticals and transoms of strength and stiffness sufficient to restrain
+it from any further flexure. It will, of course, be necessary also to
+take care that the compression member is good as a strut between the
+points of restraint. A simple and sufficiently precise method of dealing
+with this question is much needed. In cases where the floor weight rests
+on the flange projection, it is also necessary to give the transom
+additional strength to an extent enabling it to resist the twisting
+effort between any two of these transverse members; further, resistance
+to wind on the girder has to be provided in both transoms and verticals.
+
+It may be hardly necessary to insist that bracing intended to stiffen a
+structure against wind, local crippling, or vibration, should be made
+complete, not stopping short at some point, because it cannot
+conveniently be carried further, as is sometimes done, unless the
+strength of those parts of the structure through which the forces from
+the bracing must be communicated to the abutments is sufficiently great,
+considered with reference to other stresses in those parts which have
+also to be endured.
+
+Bracing stopped short in this way, making only the central part of a
+bridge rigid, may have the effect of increasing the forces to which the
+unstiffened end members would otherwise be liable. Such a structure
+would evidently be much stiffer against wind-gusts than if no bracing
+existed--the resistance to a blow would be increased; but the power to
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater maximum forces than
+if bracing were wholly omitted. The net effect may still be better than
+with no bracing, the point raised being simply that of an increase of
+stress in particular end members.
+
+In the bracing of tall piers, the rising members of which will be
+subject to any considerable stress, if the diagonal members are not
+finally secured when the piers are under their full load, or an initial
+stress of proper amount induced in those members, the effect of loading
+will be to render them slack; so that an appreciable amount of movement
+at the top may occur before it can be limited by the efficient action of
+the bracings. This effect under blasts of wind or continual passage of
+trains may, indeed, be dangerous. Similar considerations apply to the
+top wind bracing of deep girder bridges, influencing also the bottom
+bracing in a contrary manner, which calls for attention in fixing the
+unit stresses for such members.
+
+The bracing of sea-piers is very liable to slacken if made with
+pin-and-eye ends, as is often done for round rods. The detail presents
+advantages in erection, but is not altogether satisfactory in practice.
+Such connections are continually working. In the finest weather, with
+the sea quite smooth but for an almost imperceptible wave movement, the
+lower parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there room for
+surprise when it is considered that these oscillations, occurring at
+about ten to each minute, never wholly cease, and amount in the course
+of one year to over five million in number.
+
+Bracing attached in such a manner that there can be no initial slack, or
+slack due to wear under endless repetitions of small amounts of stress,
+will have a much better chance to keep tight. The advantage presented
+by round rods in offering little surface to the water, is more than
+negatived by inefficiency of the usual attachments for such rods.
+
+The author has observed that bracing of members possessing some
+stiffness, and with good end attachments to ample surfaces, appears to
+stand best in ordinary sea-pier work. For such structures the bracing
+should consist of a few good members, with a solid form of attachment,
+rather than of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very possibly also, in
+the case of sea-pier work, in unskilled hands. If round rods must be
+used, they will stand much better if made of large diameter.
+
+Before leaving the subject of bracing, it may not be out of place to
+refer to wind pressure, as this may so much affect the proportioning of
+the members.
+
+Some years since the author had occasion to examine a number of
+structures with respect to their stability. Of foot-bridges from 60 feet
+to 120 feet long, three or four, when calculated on the basis
+recommended by the Board of Trade as to pressures upon open-work
+structures, worked out at an overturning pressure of from 18 lb. to 22
+lb. per square foot. These bridges had been many years in existence; it
+is, therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them as to the
+whole surface.
+
+[Illustration: FIG. 28.]
+
+Particulars were taken in 1895 of a notice-board, presenting about 12
+square feet of surface, which was blown down in the great storm of March
+24 of that year, at Bilston, in Staffordshire. It was situated at the
+foot of a slight slope, over which the wind came, striking the
+obstruction at right angles. The board was mounted on two oak posts of
+fair quality and condition, which broke near the ground at bolt holes
+(see Fig. 28). The force required to do this, at 9000 lb. modulus of
+rupture--a moderate value--corresponds to 50 lb. per square foot on the
+surface exposed above the break.
+
+In the same neighbourhood, at the same time, considerable damage was
+wrought in overturning chimney stacks, to buildings and roofs; the
+general impression in the locality being that the storm was of
+exceptional, even unprecedented, violence. Bilston, it should be noted,
+lies high.
+
+At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27
+lb. was registered. In another part of the country it is said to have
+been 37 lb. Wind is so capricious in its effects over small areas as to
+render it probable that the maximum pressures have never been recorded;
+but this is a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by themselves
+insufficient to throw much light on the question, may be of use in
+connection with other known examples.
+
+
+
+
+CHAPTER V.
+
+RIVETED CONNECTIONS.
+
+
+Considerable latitude is observable in the practice of engineers in the
+use of rivets. Numberless experiments to determine the resistance of
+riveted connections have from time to time been made, but these are not
+to be considered by themselves as final, when the results of experience
+in actual construction, are available for further enlightenment.
+
+The class of workmanship so largely influences the degree in which
+rivets will maintain their integrity that it is only by the observation
+of a large number of cases, including all degrees of workmanship, that
+any reliable conclusions may be drawn. In this respect laboratory
+experiments have an apparent advantage, as the conditions may be kept
+sensibly the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must in the end
+determine the utility of any inquiry for practical application.
+
+The author has studied the particulars of a number of cases to ascertain
+under what conditions as to stress, having due regard to the effects of
+vibration, rivets will remain tight, or become loose. Every loose rivet
+that may be found cannot, of course, be taken as being due to excessive
+stress; the more frequent cause is indifferent work, evidenced by the
+fact that neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon the
+remainder. When rivets loosen as the direct result of over-stress, it is
+usually by compression of the shank and enlargement of the hole, or by
+stretching of the rivet and reduction of its diameter. Instances of
+failure by partial or complete shear are extremely rare; indeed, the
+author has never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work, it is not
+uncommon to find it cut or bent as an after consequence.
+
+In estimating stresses at which rivets have remained tight, or loosened,
+as the case may be, examples have generally been chosen in which there
+could be no reasonable doubt as to the amount of those stresses by the
+ordinary methods of computation. This is clearly most important, as, if
+any appreciable uncertainty remained as to the degree of stress, the
+results deduced would be of little value. For this reason those
+instances in which the loads upon girders, or parts of girders, may find
+their way to the supports by more than one route, are to be regarded
+with caution, as are those in which full loading possibly never obtains,
+but which may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been used in
+making the computations; in some cases from direct measurement from
+particular rivets, in others with a suitable allowance for excess
+diameter of hole, according to the class of work under consideration.
+
+Dealing first with main girders, it may be said that rivets attaching
+the webs of plate girders to the flange angles rarely loosen, though
+subject to considerable stress. In illustration of this may be named a
+bridge for two lines of way, 85 feet effective span, having two main
+girders with plate webs, and cross-girders resting on the top flanges,
+previously referred to (see Fig. 26).
+
+The girders, which were 6 feet 9 inches deep, had a bearing upon the
+abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches
+pitch. There is in a case of this kind some little uncertainty as to
+what is the stress on the flange angle rivets at, or very near to, the
+bearings; but, taking the vertical rows of rivets at the web joints near
+the ends as presenting less uncertainty, the stress per rivet works out
+at 4·8 tons, being 4 tons per square inch on each shear surface, and 11
+tons per square inch bearing pressure upon the shank in the web plate,
+which was barely 1/2 inch thick. This bridge was frequently loaded upon
+both roads, but with one road only carrying live load, the stresses in
+the more heavily loaded girder would be fully 90 per cent. of those
+obtaining as a maximum. There was on this bridge, which had been in use
+31 years, considerable movement and vibration.
+
+It is by no means uncommon to find cases of rivets in main girders
+taking 11 tons per square inch bearing pressure--occasionally more--and
+remaining tight. As furnishing an instructive, though slightly
+ambiguous, instance of rivets in single shear, may be cited a bridge not
+greatly less than that just referred to, of about 65 feet span, carrying
+two lines of way, there being two outer and one centre main girder of
+multiple lattice type, with cross-girders in one length 4 feet apart,
+riveted to the bottom booms of the main girders; these rivets, by the
+way, were in tension. The floor was plated, the road consisting of stout
+timber longitudinals, chairs, and rails (Fig. 29).
+
+[Illustration: FIG. 29.]
+
+It should be noted that there is in this case some difficulty in
+ascertaining the precise behaviour of the cross-girders, affecting the
+proportion of load carried by the outer and the inner main girders.
+Strict continuity of all the cross-girders could only obtain if the
+deflection of the main girders were such as to keep the three points of
+suspension of each cross-girder in the same straight line. A close
+inquiry showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would, under load,
+by relative depression of the middle point of support, be reduced to
+the condition of two simple beams, those at the extreme ends of the span
+would behave as continuous girders.
+
+With both roads carrying engine loads equal to those coming upon the
+bridge, the author estimates that for the centre main girder the shear
+on the rivets of the end diagonals, secured by one rivet only, was 14·9
+tons per square inch, and the bearing pressure 16·3 tons; the flange
+stress being 7·1 tons per square inch net. The outer main girders are
+most heavily stressed when but one road, next to the outer girder
+considered, carries live load. For this condition the stresses work out
+at 9 tons per square inch shear on the rivets of the end diagonals, and
+9 tons bearing pressure, the flange stress being 5·7 tons per square
+inch on the net section.
+
+Without intending to throw any doubt upon the substantial truth of these
+results, it must be admitted that instances of greater simplicity of
+stress determination are much to be preferred. For purposes of
+comparison, but not as having any other value, the results have also
+been worked out on the supposition of all cross-girders acting each as
+two simple beams, and also for strict continuity, and are here
+tabulated, together with the conclusions given above.
+
+The cross-girders were moderately stressed, and the tension on the
+rivets attaching them to the main girders probably did not exceed 3 tons
+per square inch.
+
+It should be pointed out that the traffic over the bridge was small. The
+centre main girder but seldom bore its full load, though at all times
+liable to receive it. Much importance cannot, therefore, be attached to
+the results for this girder, other than as showing how a structure may
+stand for many years, though liable at any time to the development of
+stresses which would commonly be regarded as destructive, or nearly so.
+
+EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS.
+
+  ---------------------------------+-----------+------------+---------
+                                   |   Cross-  |   Cross-   |
+                                   |  Girders  | Girders as | Correct
+                                   | as Simple | Continuous | Results.
+                  --               |   Beams.  |   Beams.   |
+                                   +-----------+------------+---------
+                                   | Stress in Tons per Square Inch.
+  ---------------------------------+-----------+------------+---------
+  Centre girder, 63 ft. span (both |           |            |
+  roads loaded):                   |           |            |
+    Rivets in diagonals--Shear     |    13·7   |    17·2    |  14·9
+          Do.            Bearing   |           |            |
+                         pressure  |    15·0   |    18·8    |  16·3
+                         Flange    |           |            |
+                         stress    |     6·8   |     8·5    |   7·1
+                                   |           |            |
+  Outer girder, 66 ft. span (near  |           |            |
+  road loaded):                    |           |            |
+    Rivets in diagonals--Shear     |     9·6   |     8·2    |   9·0
+          Do.            Bearing   |           |            |
+                         pressure  |     9·6   |     8·2    |   9·0
+                         Flange    |           |            |
+                         stress    |     5·9   |     5·1    |   5·7
+  ---------------------------------+-----------+------------+---------
+
+The material and workmanship of the bridge were good. The rivets of the
+centre girder end diagonals, 1 inch in diameter, were originally 7/8
+inch, but on becoming loose were cut out, the holes reamered, and
+replaced by the larger size, which remained tight, and to which the
+stress figures apply. The rivets in the diagonals near the centre, 7/8
+inch in diameter, which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The riveting in the
+outer girder diagonals, subject to smaller stresses, much more
+frequently developed, also gave trouble, particularly those liable to
+counter stresses.
+
+Apart from looseness of rivets, the general appearance and behaviour of
+the bridge, which had been in existence about twenty years, was not
+suggestive of any weakness.
+
+Of smaller girders, an example showing the necessity for care in
+discriminating, if it be possible, between looseness of rivets resulting
+from over-stress and that due to other influences may first be quoted.
+Two trough girders, of 11 feet effective span, each of the section shown
+in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle,
+with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch
+pitch, showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (Fig. 31). From the nature of the
+arrangement the lower web rivets, which were loose, would receive the
+first shock of the load coming upon the span, but there were evidences
+indicative of original bad work. The angle bars gaped, suggesting that
+these had first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets failing to
+pull the work close, and then readily working loose. Here there is
+considerable uncertainty as to how much of the loosening is to be
+attributed to bad work, and how much to stress. It may, however, be
+remarked that whatever bearing stress was the ultimate result of the
+load hammering on the lower angle flanges, loosening rivets never
+perhaps really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable
+impactive force, was not sufficient to loosen these. The girders were
+taken out after being in place sixteen years.
+
+[Illustration: FIG. 32.]
+
+[Illustration: FIG. 30.]
+
+[Illustration: FIG. 31.]
+
+An instance of undoubted excessive bearing pressure was found in the
+cross-girders of a bridge, mentioned on p. 15, of which so many web
+plates were cracked. This bridge, carrying two lines of way, had outer
+main girders, and long cross-girders with 1/4-inch webs and 3/4-inch
+rivets, 4 inches pitch. The rivet stresses work out at 4·3 tons per
+square inch on each shear surface, and 24 tons per square inch bearing
+pressure. For one road only being loaded, the latter figure falls to
+18·5 tons. The traffic over this bridge, twenty years old, was
+considerable, rapid, and heavy. It is hardly necessary to add that a
+large number of the rivets were loose, one of which is shown in Fig. 32.
+
+[Illustration: FIG. 33.]
+
+To take another case relating to a floor system of extremely bad design
+(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor
+having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches
+deep, supporting hog-backed trough longitudinals. The cross-girders were
+at their ends but 6-3/4 inches deep, the distance from the bearing of
+cross-girders to centre of longitudinals carrying a rail being 2 feet 10
+inches, in which length were eight rivets in the web and angles at the
+top, and six at the bottom, all 3/4 inch in diameter.
+
+The shear stress on the upper rivets works out at 7·3 tons per square
+inch on each shear surface, the bearing pressure 20·6 tons per square
+inch. On the lower rivets the shear stress becomes 9·7 tons, and the
+bearing pressure 27·4 tons, per square inch. Care was exercised in
+computing these stresses, that part of the bending moment carried by the
+web being allowed for, but it must be admitted that the result is,
+probably, approximate only. The sketch here given shows the cross-girder
+end and section. The rivets, though in double shear, were, as might be
+expected, loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled after twelve
+years’ use.
+
+In illustration of the behaviour of rivets in the ends of long
+cross-girders, both shallow and weak, and many years in use under heavy
+traffic, may be cited connections having end angle bars to the
+cross-girders, with six rivets through the web of main girders. The
+bearing pressure worked out at 7·8 tons per square inch. Many rivets
+were loose, but it should be remarked that the workmanship was not of
+the best class, and the cross girders flexible: a characteristic very
+trying to end rivets, and inducing a stretch in some, already referred
+to as a possible cause of loosening. This will be apparent if the
+probable end slope of weak girders be considered. The author concludes
+that this inclination should not, for ordinary cases, exceed 1 in 250;
+but the ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly regarded as bad
+practice to submit rivets to tension, yet this is frequently, though
+unintentionally, permitted in end attachments, without any attempt to
+limit the amount of tension. With suitable restrictions, there appears
+no serious objection to rivet tension for many situations.
+
+Another instance of cross-girder end connections of a different type is
+illustrated in Fig. 34.
+
+The main girders of the bridge were 12 feet apart, each cross-girder end
+carrying its share of the half of one road. The mean bearing pressure
+upon the rivet shanks works out at 5·8 tons per square inch for the six
+rivets of the original joint, but in the particular joint shown some of
+the rivets had loosened, making the bearing pressure upon the remainder
+about 8·7 tons per square inch. It is apparent there must have been
+considerable stress on the top and bottom rivets which loosened. These
+two rivets would also, because of difficult access, be in all likelihood
+insufficiently hammered up. The joints worked rather badly; the loose
+rivets had “cut” to a considerable extent, a process materially assisted
+by the gritty nature of the ballast (limestone), particles of which,
+getting into the joint, contributed to the sawing action; this had
+clearly been taking effect for some considerable time. (See Fig. 35.)
+
+[Illustration: FIG. 34.]
+
+[Illustration: FIG. 35.]
+
+The two cases of cross-girder ends given are both rather exceptional in
+character, and in each case the defects appear to be due to general bad
+design and workmanship rather than to any serious excess of bearing
+pressure. This may be illustrated by taking the common case of
+cross-girders, 2 feet deep, carrying two roads, and having end angle
+irons riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which is, for old
+work, simply typical, and does not relate to any specific instance, the
+bearing pressure on the rivets will work out at from 6 to 8 tons per
+square inch, and will seldom be accompanied by looseness of rivets, and
+then only as a result of faulty work.
+
+Some sketches of rivets taken from old bridges have already been given
+in connection with the cases to which they belong; a few others are here
+shown (Figs. 36 to 40) to further illustrate what may be the actual
+condition of rivets after some years’ use, and how different from the
+ideal rivet upon which calculations are based. These are, however, bad
+instances.
+
+[Illustration: FIG. 36.]
+
+[Illustration: FIG. 37.]
+
+[Illustration: FIG. 38.]
+
+[Illustration: FIG. 39.]
+
+[Illustration: FIG. 40.]
+
+It should be noticed that rivets may, if in double shear, be loose in
+the middle thickness, due to enlargement of the hole in the central part
+and compression of the rivet, and yet show no sign of this by testing
+with the hammer. There is, however, generally marked evidence of another
+kind in the “working” of the inner part, as, for instance, the web of a
+plate girder, in which case a discoloration due to rust is to be found
+along the edges of the angle bars, or a movement may be detected on the
+passage of live load. Red rust is, in fact, frequently an indication of
+something wrong, when no other evidence is apparent. In plate girders
+having [T] or [L] bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching these
+bars to the cross-girder tops loose, due to causes already dealt with.
+The riveted connection should, as to strength, bear some relation to the
+strength and stiffness of the parts secured, if the rivets are to remain
+sound.
+
+It may be well to give here a summarised statement of the results
+already named, for purposes of ready reference. These by themselves are
+not sufficient to enable working stresses to be deduced, though they are
+instructive. The author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which the rivets
+behaved well, but is not now able to give precise particulars of these.
+
+EXAMPLES OF RIVET STRESSES.
+
+  ---------+-----+---------+------+------+--------+-----------------
+     --    |Span |  Where  |Shear |Single|Bearing | Tight or Loose.
+           | in  |  Found. |Stress|  or  |Pressure|
+           |Feet.|         |  in  |Double|in Tons |
+           |     |         | Tons |Shear.|  per   |
+           |     |         |  per |      | Square |
+           |     |         |Square|      | Inch.  |
+           |     |         |Inch. |      |        |
+  ---------+-----+---------+------+------+--------+-----------------
+  Main    {|  85 |   Web   |  4·0 |   D  |  11·0  | Tight.
+  girders {|  66 |Diagonals|  9·0 |   S  |   9·0  | Many loose.
+          {|  63 |    „    | 14·9 |   S  |  16·3  | Tight generally.
+           |     |         |      |      |        |
+          {|  11 |   Web   |  1·4 |   D  |   7·0  | Tight.
+  Small   {|  26 |    „    |  4·3 |   D  |  24·0  | Many loose.
+  girders {|  11 |    „    |  7·3 |   D  |  20·6  | Loose.
+          {|  11 |    „    |  9·7 |   D  |  27·4  | Loose.
+           |     |         |      |      |        |
+  End     {|  27 |   Ends  |  5·4 |   S  |   7·8  | Loose.
+  connec- {|  12 |    „    |  1·8 |   D  |  {5·8  |}Many loose.
+  tions   {|     |         |      |      |  {8·7  |}
+           |     |         |      |      |        |
+  (Type    |     |         |      |      |        |
+  case)    |  26 |    „    |  4·8 |   S  |   7·0  | Tight.
+  ---------+-----+---------+------+------+--------+-----------------
+
+It is probable that the fact of a rivet being in single or in double
+shear largely affects its ability to resist the effects of bearing
+pressure, as commonly estimated. In the first case, the rivet-shank must
+bear heavily on the half-thickness of the plates or bars through which
+it passes, rather than on the whole thickness; and it is to be supposed
+that under this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.
+
+[Illustration: FIG. 41.]
+
+[Illustration: FIG. 42.]
+
+The author has no very definite information in support of this
+contention, but suggests that for double shear the permissible bearing
+pressure may probably be as much as 50 per cent. greater than for rivets
+in single shear; the difference being made rather in the direction of
+increasing the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this is evident when
+it is considered that the practice has commonly been to make no
+distinction, so that whatever bearing pressures are found to be
+sufficient for both cases may be increased for those capable of taking
+the greater amount. Figs. 41 and 42, here given, illustrate the
+behaviour of rivets under the two conditions.
+
+With reference to the amounts of the stresses to which rivets may be
+subject, the author concludes, as a result of his experience, coupled
+with a consideration of known laboratory tests, that for all dead load
+these may be quite prudently higher than is frequently taken. For iron
+the shear stress to be 10 per cent. less than the stress of parts
+joined; and the bearing pressure--for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary mild
+steel the shear stress to be 20 per cent. less than the stress in parts
+connected, and the bearing pressure equal to it for single-shear rivets;
+and 50 per cent. more for rivets in double shear, though the two latter
+values may probably approach those for wrought iron in steel of the
+higher grades sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction of the
+nominal working stress, arrived at by any one of the methods in use
+which may be adopted, affecting both the parts connected, and the rivets
+connecting them. For reverse stresses it is advisable to keep the shear
+stress in any rivet so low, say 3 tons per square inch, that the
+frictional resistance of the parts gripped by the rivets shall be
+sufficient to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure that,
+if brought to a bearing in one direction by the greater force, it shall
+not go back with reversal of stress. This requirement may be open to
+some question with respect to good machine-riveted work, but for
+hand-riveted connections it may certainly be adopted with wisdom.
+
+The following table will show at a glance how the stresses proposed vary
+with the unit stresses governing the main sections.
+
+PROPOSED TABLE OF RIVET STRESSES.
+
+  -----------+-------------+----------------+----------------
+  Unit Stress|             |Bearing Pressure|Bearing Pressure
+      in     |Shear Stress.|for Single-Shear|for Double-Shear
+    Member.  |             |     Rivets.    |    Rivets.
+  -----------+-------------+----------------+----------------
+              _Wrought Iron.--Tons per Square Inch._
+       3·0   |     2·7     |       3·6      |       5·4
+       4·0   |     3·6     |       4·8      |       7·2
+       5·0   |     4·5     |       6·0      |       9·0
+       6·0   |     5·4     |       7·2      |      10·8
+       7·0   |     6·3     |       8·4      |      12·6
+                 _Steel.--Tons per Square Inch._
+       4·0   |     3·2     |       4·0      |       6·0
+       5·0   |     4·0     |       5·0      |       7·5
+       6·0   |     4·8     |       6·0      |       9·0
+       7·0   |     5·6     |       7·0      |      10·5
+       8·0   |     6·4     |       8·0      |      12·0
+       9·0   |     7·2     |       9·0      |      13·5
+  -----------+-------------+----------------+----------------
+
+  NOTE.--Tension on rivets to be limited to one-half the permissible
+  shear stress, the holes being slightly countersunk under snap-head.
+
+It may be objected that the shear stresses in the proposed table are
+somewhat high for wrought iron and steel. This feature is intentional,
+and is supported by the consideration that whereas there may be loss of
+strength in the members of a structure by waste, there is no such loss
+in rivets, if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective field rivets
+is left to be dealt with as may be considered advisable for each
+particular case, the table as it stands being applicable only to
+riveting not below the standard of first-rate hand work.
+
+Cases of loose rivets in main girders over 50 feet span, due to any
+cause but bad work, are extremely rare, unless resulting from the action
+of some other part of the structure. It may be stated broadly that for
+railway bridges of less than perfect design, the nearer the rail, the
+more loose rivets, generally at connections. This is, no doubt, largely
+due to the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead load, and
+because this effect has been but little modified by the elasticity of
+any considerable length of intervening girder-work. In addition to this,
+it is quite usual to find the rivets more heavily stressed, even though
+the load be considered as “static,” in the floor system than in the
+main-girders, though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting--viz., the
+connections--are commonly dealt with by hand; and for this reason it is
+the more necessary to design these with the greatest care.
+
+Any arrangement which favours the gradual acceptance of stress by one
+part from another will contribute to the integrity of riveted
+connections, and lessen the liability of the material to develop faults.
+In other branches of design this is well recognised, but appears in much
+old bridge work to have been entirely overlooked.
+
+Bridges carrying public roads very seldom furnish examples of loose
+rivets; the conditions are generally much more favourable, impact being
+practically absent, full loading infrequent, and the proportion of dead
+load to live, high.
+
+It is, perhaps, hardly necessary to insist upon rivets being, apart from
+mere considerations of strength, sufficiently near together to insure
+close work and exclude moisture. Outside edge seams should never be more
+widely spaced than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections, the
+greater stiffness of the section makes wider spacing allowable up to,
+say, 20 times the thickness; but this must be governed largely by the
+amount of riveting required to pull the parts close together. Where more
+than four thicknesses are to be gripped by the rivets, 3/4 inch in
+diameter is hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed 5/8 inch thick.
+
+
+
+
+CHAPTER VI.
+
+HIGH STRESS.
+
+
+High stress, provided it be well below that at which immediate injury
+results, or possible failure, is not uniformly objectionable. It may be
+first considered relative to the absolute and elastic limits of
+strength, next with respect to the range of stress, and, finally, with
+regard to the frequency of application. For practical purposes--that is,
+for the continued efficiency of a structure--the limit of elasticity
+must be considered to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long as it
+lasts, be liable to the original measure of stress. There may be places
+in a bridge, however, over-stressed only in the earlier period of its
+existence, which, by being over-stressed and suffering deformation,
+permit the origin of this distortion to be harmlessly met in some other
+way. In such a case the injury done to that part does not, of necessity,
+lead to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail after
+being in use but a short time. As for riveting, so in dealing with the
+amount of stress to which a member is supposed to be liable, it should
+be clearly understood by what method this has been arrived at, whether
+the value assigned is the actual measure of the stress, or simply the
+conventional amount arrived at in the conventional way; perhaps
+neglecting web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal amount of
+stress, or including only a partial recognition of those influences. In
+any case quoted the stress named is that at which the author arrives by
+the ordinary methods of computation carefully applied, where these
+appear to be sufficiently precise, unless any qualifying remark be
+added. Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that basis, and
+deducing the stress at the holes from the ratio of net to gross section
+at the extreme fibres; a method more correct than by reference to the
+moment of inertia of the net section. Any exhaustive refinement in the
+study of stresses is not attempted, both because it is beyond the
+author’s powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation in
+practice. Effective spans are taken at moderate values, and all
+exaggeration is avoided.
+
+The effects of impact in any part vary so much with nearness to, or
+remoteness from, the living load, and the frequency of development of
+the maximum stress from all causes acting together is so much affected
+by the same consideration, that it is apparent a nominal stress which
+may be harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as ordinarily
+stated--i.e., at so much per square inch, uniform across a section--is
+seldom a cause of trouble. In nearly all cases of failure there is an
+accompanying localised destructive stress, either in rivets or
+elsewhere, with crippling or deformation of some essential part. In the
+tension flanges of main girders with uncomplicated stress, this may run
+up to an amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the compression
+flanges, if these be in themselves sufficiently stiff, or properly
+restrained from side flexure. In support of the above statement may be
+quoted the following instances relating to wrought-iron structures:--
+
+A bridge of 60 feet effective span, having girders immediately under the
+rails, had a flange stress of 6·3 tons per square inch. Another of 64
+feet span, carrying two lines of way, with outside main girders and
+cross-girders, had the flanges of the former stressed to 6·8 tons per
+square inch. A third, of 76 feet span, of similar construction to the
+last, was stressed in the main girder flanges to 7·5 tons per square
+inch. The webs were not included in the computation; the figures,
+therefore, compare with ordinary practice. In these three cases the main
+girders showed no signs of distress, referable to the results stated,
+though the top flanges in the last case were curved inwards. The effect
+of this flexing of the flange would be, of course, to increase the
+amount of compressive stress along one edge, though to what degree
+cannot now be stated.
+
+[Illustration: FIG. 43.]
+
+[Illustration: FIG. 45.]
+
+[Illustration: FIG. 44.]
+
+A further instance of considerable flange stress occurred in a bridge of
+seven nearly equal continuous spans, 25 feet generally, the end and
+greatest span being 29 feet 6 inches, centre to centre of bearings. Some
+details of the bridge are given in Figs. 43 to 45. The four inner main
+girders under rails were 2 feet deep, with webs 1/2 inch thick over
+piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3
+inches by 3 inches by 5/8 inch. There were also two outer girders of the
+same depth, with single [L] bars. Plate diaphragms of full girder depth
+and particularly stiff were carried right across the bridge at the
+centre of the spans, and over the piers. The girders, though evidently
+designed to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see Fig. 45). It is
+doubtful if the girders acted with strict continuity for long after
+erection, as the excessive stress in the rivets of the flange joint
+would, for that condition, have been nearly sufficient to shear them. It
+is probable that this being so, the joints first yielded, relieving the
+bending moment over the piers, and increasing it near mid-span. Whether
+the end spans be considered as strictly continuous with the rest, or as
+simple beams, the maximum bending moments would not greatly differ,
+though occurring for continuity over the pier, for free beams at the
+centre. There is, however, an intermediate condition which makes the
+moments at these two places less than either maximum, but equal to each
+other; a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been calculated,
+giving the minimum stress value that can be accepted. The diaphragm has
+been assumed to transfer to the outer girders a due proportion of the
+load. With this explanation it may now be stated that, under engine
+loads corresponding to those running, the flange stress worked out at
+7·4 tons per square inch tension, web included, or 9·7 tons per square
+inch without considering the web; which stresses, it is more than
+probable, may have been greater. The figures include the consideration
+of anything which may contribute to lowering the stress, and are hardly
+to be compared with those worked to in ordinary design of new work, in
+which it would be quite usual to neglect the assistance of the outer
+girders and the webs, to work to heaviest engine-loads, and possibly
+include an allowance for the effects of settlement. Dealt with in this
+way the girders would seem to be of about one-fourth the strength that
+would be required in the design of a new bridge, in which certain
+elements of strength would be deliberately ignored.
+
+The ironwork was in good condition, there was no ordinary evidence of
+weakness apart from the calculated results, the vibration was distinctly
+moderate, and the deflection, though not recorded, was certainly small.
+The bridge did, indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long overstressed
+may have a sensibly higher modulus of elasticity than newer work at more
+moderate stresses. The traffic was not very considerable, and both
+roads, of the same spans, but seldom loaded at the same time; though
+with this construction of bridge there would in either case be very
+little difference. The author recalls no reason for supposing that the
+piers had yielded in any sensible degree. The bridge was rebuilt after
+some thirty-six years’ use.
+
+Stress of considerable amount in the flanges of a latticed main girder
+of 63 feet span has already been noticed in the chapter on “Riveted
+Connections,” which for the tension boom worked out to 7·1 tons per
+square inch, the flanges in this case showing no signs of weakness. An
+instance has also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons per square
+inch, the girder recovering its form when relieved of load.
+
+As to stress in cross-girder flanges, an example may be quoted of a
+bridge of 109 feet span, carrying two roads, having outside main
+girders, with cross-girders between; these latter were stressed in the
+flanges to 6·7 tons per square inch (webs not included), if the partial
+distribution among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some reason to
+think in this instance that distribution had the effect of reducing the
+stress quoted, as the observed deflection of the cross-girders was
+materially less than that calculated for girders acting independently of
+each other, though this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the heavy main
+girders, would also tend to moderate the stress. No very definite
+conclusion can therefore be deduced from this instance.
+
+To take another case of less uncertainty, the bridge of 35 feet span
+(see Fig. 33), referred to in “Riveted Connections,” may again be cited.
+The extreme fibre stress in the cross-girder flanges worked out at 6·3
+tons per square inch, web included, or 6·5 tons, exclusive of the web.
+It cannot be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was 1/2 inch on the span of
+11 feet, in addition to a permanent set of 3/4 inch, largely due,
+however, to “working” rivets.
+
+A better and altogether conclusive case of the way in which
+cross-girders may occasionally suffer considerable stress, and show no
+sign, is furnished by two cross-girders, of which some particulars are
+here given. These girders occurred in the floor of a very acute angled
+skew bridge, riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end on a masonry
+abutment. The first girder was about 19 feet effective span, 12 inches
+deep in the web, with angle bar and plate flanges. The girders were
+spaced 6 feet apart, and were connected under the rails by [T]-bars,
+cranked down to face the webs, and riveted through. Though these [T]’s
+had little stiffness, yet the frequent vertical movements of the girders
+relative to each other, under passing loads, had broken the majority of
+the [T]-bars at the bends, so that no notice need be taken of these as
+transferring load from any one cross-girder to its neighbour. The floor
+covering consisted of timbers about 4 inches thick, also incompetent to
+transfer any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers, chairs,
+and ordinary bull-headed rails. The stress to which the girder was
+liable works out at 8·4 tons per square inch, on the extreme fibres of
+the net section, web included; or 9·1 tons, neglecting the web, under
+engine-loads of a common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with angle bar
+and plate flanges. The stress per square inch was 10·5 tons, web
+included, or 11·1 tons per square inch, neglecting the web. This girder
+carried three rails, one of which was near to the abutment bearing, so
+that there was no great difference in the stress induced whether all
+three rails were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a common
+occurrence for the girders to take the full loads. The heavier engines
+passed scores of times in a day--lighter engines probably one hundred
+times. The bridge was about twenty years old, yet these cross-girders,
+when removed, showed no other sign of age and wear than that due to
+rust.
+
+[Illustration: FIG. 46.]
+
+All the foregoing instances relate to wrought-iron bridges. Two cases of
+steel construction are here added, the first of these furnishing an
+example of high girder stress somewhat remarkable. This was found in a
+trough girder of a strange pattern, of which a section is here given
+(Fig. 46). The bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a crawling
+pace. The larger of the two girders carrying the rails was 15 feet 8
+inches effective span. The sides of the trough consisted each of two
+vertical plates, originally 1/2 inch thick, but wasted to an aggregate
+thickness of 5/8 inch. These plates 6 inches deep, were connected at
+their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which
+again were riveted to a bottom plate 16 inches wide, originally 1/2 inch
+thick, wasted to 3/8 inch. Lying in the bottom of the trough, and
+riveted through the inner angle flanges, was a bridge-rail. Assuming
+that the metal retained its elastic properties from top to bottom of the
+section, at whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the net section.
+As puddled steel, of which the girders were made, may have a tenacity of
+45 to 55 tons per square inch, the assumption is probably correct. The
+author has no record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine passing over,
+required some determination.
+
+A point of additional interest in this little bridge is that, though
+made of steel, it dates as far back as 1861, having been in use
+thirty-two years when removed. The particular variety of steel used was
+known as Firth’s puddled. The evidence of this consists in
+correspondence showing that permission had been asked of the controlling
+authority, by the only users of the siding, to apply this material, with
+no evidence of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some girders of
+considerable span. The appearance of the trough girders to which the
+foregoing particulars apply was distinctly different to that which might
+be expected in ordinary wrought iron. The top edges of the vertical
+plates were wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which the girders
+held up to their work for so long is, by itself, conclusive on the
+point. The bridge-rail appeared to be of wrought iron, the different
+modulus of elasticity of which has been included in the calculation upon
+which the preceding results are based. That these girders stood so well
+is, perhaps, largely due to the fact that the load carried by them was,
+though varying within wide limits, practically free from impact, which,
+had the load passed over quickly, would, with girders so small, shallow
+and flexible, have been very sensible.
+
+The second instance of steel construction in which somewhat high stress
+is manifest is that of some steel troughing of the Lindsay pattern, used
+in a bridge built in 1885. The troughs ran parallel to the rails, having
+an effective span of 18 feet 8 inches. The depth of the section (which
+is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span
+of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.
+
+[Illustration: FIG. 47.]
+
+Assuming this to be carried on six troughs, which corresponds to 11 feet
+3 inches of width, the extreme fibre stress works out at 7·5 tons per
+square inch, under usual engine-loads. The bridge when examined after
+fourteen years’ use was in good condition, and at that time but little
+rusted; but the end seam rivets were, as is not uncommon with such
+troughing, loose. The traffic over the bridge was considerable, but not
+at great speed.
+
+On the opposite page are set out the results which have been given, in
+tabulated form, as was done for rivet stresses, to enable ready
+comparison to be made.
+
+EXAMPLES OF HIGH STRESS.
+
+  --------------+-----+---------+---------------+--------+-----------
+                |Span |  Part   |  Stress per   |Tension |Condition.
+                | in  |Stressed.|  Square Inch. |   or   |
+                |Feet.|         +-------+-------+Compres-|
+       --       |     |         | Webs  | Webs  | sion.  |
+                |     |         |  In-  |  not  |        |
+                |     |         |cluded.|  In-  |        |
+                |     |         |       |cluded.|        |
+  --------------+-----+---------+-------+-------+--------+-----------
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |60·0 |Flange   |   ..  |  6·3  |Tension | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |64·0 |   „     |   ..  |  6·8  |   „    | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |76·0 |   „     |   ..  |  7·5  |   „    | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |    {|   „     |  7·4  |  9·7  |   „    |}
+  main girders, |29·5{|   „     |  6·3  |  8·3} |Compres-|}Good.
+  plate         |    {|         |       |     } |sion    |}
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |63·0 |   „     |      7·1      |Tension | Fair.
+  lattice       |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |47·0 |Flange   | 10·0  |   ..  |Compres-| Fair.
+  plate         |     |edge     |       |       |sion    |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|26·0 |Flange   |   ..  |  6·7  |Tension | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|11.0 |   „     |  6·3  |  6·5  |   „    | Bad; loose
+  plate         |     |         |       |       |        | rivets.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|19·0 |   „     |  8·4  |  9·1  |   „    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|22·0 |   „     | 10·5  | 11·1  |   „    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Steel trough  |    {|   „     |     15·0      |   „    |}Fair,
+  girder        |15.7{|Top edge |     32·0      |Compres-|}but
+                |    {|         |       |       |sion    |}rusted.
+                |     |         |       |       |        |
+  Steel         |18·7 |Flanges  |  7·5  |   ..  |Tension | Fair,
+  troughing     |     |         |       |       |and Com-| but
+                |     |         |       |       |pression| rusted.
+  --------------+-----+---------+-------+-------+--------+-----------
+
+It would be unwise to infer from the instances which have been quoted
+that high stress may be regarded with complaisance. In the most
+conscientious engineering work there should still be a liberal margin
+for material possibly defective, or even bad, for waste and
+deterioration, and for the aggregate effect of minor errors in design,
+any one of which considerations, except the first, by itself might not
+be of great importance. The conclusion which may, however, be derived
+from this and the previous chapters is, that bridge failures are less
+likely to occur from high stress of a kind readily calculated than from
+failure in detail, obscure and little suspected, the reason for which is
+not perhaps apparent, till the attention is forcibly directed to it by
+the refusal of the structure to sustain the forces to which it may be
+liable.
+
+
+
+
+CHAPTER VII.
+
+DEFORMATIONS.
+
+
+Instructive lessons are to be had from a study of the various
+alterations in form to which metallic bridgework is liable, which
+alterations may be due simply to the development of stress of ordinary
+amount, and are then generally small; or to abnormal stresses, the
+result of some distortion in the bridge structure itself not originally
+intended, and possibly extreme. In addition to these there may be
+deformations due to settlement, to “creeping” of parts of the structure
+relative to the rest, to temperature changes, to rust, and to original
+bad workmanship. In any instance quoted below the methods adopted to
+ascertain the amounts of such alterations were quite simple, even crude;
+but as care was exercised, and no attempt made to measure any very
+minute changes, the results may be accepted as practically correct.
+
+Dismissing for the present changes of form such as are to be expected,
+and touched upon in other places in this work, with respect to the
+particular parts of bridge structures affected by them, a few instances
+will be adduced of alterations which, though not very surprising, are
+such as in the design of the work are hardly likely, in most instances,
+to have been contemplated.
+
+A case has already been referred to in which, owing to eccentric loading
+of main girders, these were, as to the top flanges, flexed sideways a
+considerable amount. It is proposed to supplement this by further
+remarks relative to somewhat similar cases. A like effect is frequently
+to be observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting ledges
+formed by the bottom angle-bars of such troughs. In old forms of this
+arrangement it is common to find the two girders forming the trough
+connected only by bolts passing through the timbers, or just above them
+and below the rails; or connected by narrow strips, which serve no other
+purpose than to prevent the sides spreading at the bottom. The top
+flanges in such cases commonly curve inwards on the passage of the
+running load, accompanied of necessity by an increase of compressive
+stress upon the outer edges of the flanges, and perhaps by the working
+of any flange-joint which may exist. This, both as to flexing of the top
+flange and the working of a joint, was noticed in the case of a bridge
+twenty-three years old, very similar to that illustrated in Figs. 8 and
+9, and described on pages 13 and 14. The top flange consisted, however,
+of a bridge rail riveted to the top edge of the web, butting at a joint,
+and covered by thick cover strips (see Fig. 48). The joint itself was
+poor, and depended largely upon the character of the butt, which was not
+sufficiently good to prevent the top member kinking at this point, under
+the joint influence of transverse effort and compressive stress, with
+possibly some help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked in passing that it is
+very objectionable to use bolts as was done in this instance; for as the
+timber settles down on its seat, taking the bolts with it, these bear
+hard in the webs, enlarging or even, as in this case, tearing the holes,
+accompanied by injury to the bolts themselves. The practice is now
+almost obsolete, but the example is instructive as showing the
+impropriety of securing timbers by bolts passing through them at right
+angles to the action of the load, unless these bolts are quite free to
+move with the timber as it compresses.
+
+If trough girders must be used, the better plan is to connect the two
+sides by a continuous bottom plate, the trough thus formed being
+properly drained, if the timber is not bedded in asphalt concrete; or to
+introduce stiff diaphragms at intervals beneath timbers, if the depth
+suffices.
+
+In the case just quoted the curvature of the top members of the girders
+was inwards, but in the instance given below, of twin girders 26 feet
+effective span, with longitudinal timbers between, resting, as before,
+upon the inner ledge formed by the bottom flanges, the curvature was
+observed in three out of four girders to be 1/2 inch in a contrary
+direction, the fourth remaining straight.
+
+[Illustration: FIG. 48.]
+
+[Illustration: FIG. 49.]
+
+An inspection of the accompanying section, Fig. 49, will, perhaps,
+render the reason evident when it is noticed that the top members are
+very unsymmetrical in form, the effect of this being to give these
+members, under stress, a strong tendency to flex outwards, apparently
+more than sufficient to counteract the tendency of an eccentric
+application of load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be not
+materially in excess, and is actually so, only because the thinness of
+the web--1/4 inch--renders it incompetent to keep the bottom flange up
+to its work, and so secure the full effect of the eccentric loading in
+limiting the outward tendency, due to the section of the top member,
+the effects of which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange to the other
+prevent the want of symmetry noticed in these--which, by the way, is on
+the wrong side for utility--from having any particular effect.
+
+To give one other example of the consequences of eccentric loading, a
+bridge of 48 feet effective span may be quoted. This bridge carried four
+lines of way supported by five main girders, trussed by kicking-struts
+in such a manner as to form a bastard arch. A part section and plan are
+given in Figs. 50 and 51.
+
+[Illustration: FIG. 50.]
+
+[Illustration: FIG. 51.]
+
+The floor consisted of Lindsay’s troughing resting upon the lower
+flanges of the main girders, the three middle girders, subject to
+eccentric loading, sometimes on one side, sometimes on the other, were,
+with dead load only, straight; but the two outer girders, liable to
+loading only on one side, had, under repeated applications of such a
+load, assumed a permanent curve towards the rails--13/16 inch in one
+case and 1 inch in the other--which curvature, no doubt, increased when
+a live load came upon the contiguous roads, though this was not
+measured. It should be remarked in passing that, owing to settlement and
+the canting of the abutments, the three middle girders were also
+“down”--in one case 3/4 inch. The girders, with one near road loaded,
+deflected 1/8 inch--greatly less than would have been the case had the
+main girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.
+
+Deformations due to settlement may be very considerable. The author
+recalls two instances affecting continuous girders. In the first of
+these, a bridge twenty years old, of two spans of about 50 feet each,
+and with girders 4 feet 6 inches deep, the centre pier had sunk 4
+inches, reducing the spans, as respects the dead load, practically to
+the condition of simple beams, just resting, but hardly bearing, upon
+the piers when free of live load.
+
+In the second case, also of two openings of about 55 feet each, with
+girders 8 feet deep, one abutment had sunk about 3 inches, more than
+doubling the stresses over the centre pier. It is manifest that
+continuous girders should only be adopted where settlement of the
+supporting points is not likely to occur to any material degree. If this
+cannot be relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to make a liberal
+allowance for settlement stresses, in which case any economical
+advantage that should exist will probably disappear. It is, however, to
+be acknowledged that so long as the girders are in touch, under dead
+load, with the bearings intended to support them, the stresses due to a
+live load are unaltered, the principal effect in this case being that
+the variation in stress due to the live load ranges between limits that
+are higher or lower in the scale of stress than is the case with
+bearings undisturbed; still, if it is desired that the maximum stress
+shall not exceed, say, 6 tons per square inch, it can hardly be a matter
+of indifference that settlement shall induce a maximum of, perhaps, 10
+tons, as in that case the stress must be 4 tons nearer the limit of
+statical strength.
+
+Before leaving this matter it may be well to point out that in the case
+of continuous girders of uniform section a moderate settlement of the
+piers may even be advantageous by reducing the moments over the piers,
+and possibly making them equal to those obtaining near the middle of the
+spans, in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.
+
+Bridges consisting of simple main girders connected by cross-girders may
+be very prejudicially affected by unequal settlement; for instance, if
+one girder bearing settles more than the others, a twist is put upon the
+structure very trying to the floor-girder connections, and possibly to
+the main girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments. Indeed,
+settlement of this kind may be much more destructive to a metallic
+bridge than to an arch of brick or masonry, the commonly accepted
+opinion notwithstanding.
+
+Instances of deformations due to the creeping of some part of the
+structure away from its work, are within the author’s knowledge, rare;
+except in the case of the ends of main girders in skew bridges, already
+referred to.
+
+Distortion, the result of temperature changes, is frequently to be
+observed in any considerable length of girder flange or parapet where
+there is not freedom of movement, unless due provision is made to check
+it.
+
+It is quite common to see parapets out of line, either because the ends
+are not free, or because the light work of the parapet being more
+exposed to the sun’s rays than the girder work to which the lower part
+is attached, expanding to a greater degree, is subject to considerable
+compressive force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or flexible
+joints at moderate distances apart, or to make the parapet sufficiently
+stiff to take the stresses developed, without crippling. A parapet may
+also go out of shape if directly attached to the top flange of a girder
+liable to heavy loading, particularly if the girder be shallower than
+the parapet, simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the girder
+proper.
+
+Rivets spaced too far apart, by allowing the plates or other parts to
+spring open slightly, and permitting moisture to enter, results in the
+growth of rust, which, as it swells in forming, forces the parts
+asunder, and may set up considerable stress.
+
+Flat bars riveted together by rivets spaced 12 inches apart may from
+this cause be forced asunder, as much as 1/2 inch, sufficient to set up
+a stress, with any practicable thickness of bar, much exceeding the
+elastic limit.
+
+Local distortions may occur as the result of imperfect workmanship or
+careless erection, causing quite possibly very severe local stresses; or
+girder flanges may be out of straight as a result of riveting up along
+one side first, instead of advancing the riveting simultaneously along
+the whole breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is sometimes
+done to girderwork during manufacture by rough treatment to make the
+work come together; but the author has little to offer with respect to
+these matters that is not common knowledge. It may, however, be pointed
+out in passing that a bridge upon the design of which great care has
+been expended, with the idea that theoretical propriety shall not be
+violated, may be completely spoiled in this respect by careless
+construction. Fortunately, both steel and wrought iron, if of good
+quality, are long suffering. Incompetent erection will sometimes result
+in the true girder camber not appearing, or in differences as between
+girders supposed to be similar. This is not, of course, a deformation in
+the sense in which the word has previously been used, but it is
+desirable to bear the fact in mind as a possible cause of defective
+camber in dealing with questions of deformation.
+
+The foregoing has reference chiefly to alterations of form in bridgework
+of wrought iron or steel, but a case of considerable interest is that of
+a cast-iron arched structure, of which the author made a very complete
+examination.
+
+[Illustration: FIG. 52.]
+
+[Illustration: FIG. 53.]
+
+This bridge, built in 1839, and carrying two lines of railway, consisted
+of three spans, 100 feet each, of 10 feet rise, made up of four inner
+and two outer ribs, each rib being in three nearly equal parts; the
+floor was of timber, the abutments and piers of masonry. As originally
+constructed there was no bracing between the ribs other than the frames
+indicated on the plan here given (Fig. 52), stretching from outer rib
+to outer rib in the neighbourhood of the rib joints, which were simple
+butts without bolts or any equivalent means of connection. The floor
+was, however, braced in the horizontal plane, and the structure was also
+braced over the masonry piers. After forty-two years’ use supplementary
+distance-pieces were introduced between the ribs, but still no bracing
+between them, or any efficient means of checking lateral movement. A
+crack developing in one of the outer ribs at the crown, led to an
+investigation to trace the cause, the bridge then being fifty-four years
+old. Careful plumbing of the abutments revealed the fact that three out
+of four abutment pilasters were out of the vertical, as shown in Figs.
+52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner
+from which the cracked rib had its springing; there was also other
+evidence of settlement in an old crack extending from the top of the
+abutment to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were also out of
+plumb, that which was cracked being 2-1/2 inches out at the centre. The
+joints of the ribs, which, as already stated, were simple butts, in some
+cases opened and shut, as the load passed over, in such a way as to
+suggest that the ribs were acting, in a manner, as four-hinged arches,
+of which two hinges were at the springing, and the other two at the
+joints, one of which would for most positions of the load be out of use,
+reducing the rib to the three-hinged condition; in other words, as the
+rolling load passed over the span, one or other of the two joints of a
+rib would “gape” an appreciable amount at the bottom or at the top.
+Observations were taken by means of a theodolite placed below, either
+upon the bank or upon the tops of the masonry piers, sighting upon
+suitable scales attached to the ribs to ascertain the amounts of
+vertical and horizontal movement during the passage of trains over the
+bridge. The principal results are set forth in the following table:--
+
+MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT.
+SPANS.
+
+  ----------------------+-------+----------+-----------
+                        |Fall in| Rise in  | Lateral
+            --          |Inches.| Inches.  | Movement
+                        |       |          |in Inches.
+  ----------------------+-------+----------+-----------
+                      _Span No. 1._
+  At A. Up road loaded  |  ·20  |   ·08    |   ·04
+   „ A. Down road loaded|  ·08  |   ·03    |   ·04
+   „ B. Down road loaded|  ·14  |No record.|   ·02
+                      _Span No. 2._
+  At C. Up road loaded  |  ·40  |   ·13    |  Slight.
+   „ C. Down road loaded|  ·10  |   ·05    |     „
+                      _Span No. 3._
+  At D. Up road loaded  |  ·22  |No record.| No record.
+   „ D. Down road loaded|  ·15  | Slight.  |  Slight.
+  ----------------------+-------+----------+-----------
+
+  NOTE.--The lateral movements are to either side of the mean position.
+
+The particulars for spans 2 and 3 were obtained with the instrument set
+up on the pier between these spans. The tremor of this pier was such
+that no useful readings for lateral movement could be obtained. Further,
+as the rolling load came upon these spans, the effect was to rock the
+pier to an extent vitiating the readings for vertical displacement; but
+by sighting upon the fixed abutment, and observing the amount of this
+rocking, suitable corrections were made in the apparent rib movements.
+The figures given in the table are thus corrected. The pier rocking was
+equivalent, as an extreme, to an inclination from the vertical of 1 in
+3200. An attempt to measure the horizontal movement of the pier-top was
+unsuccessful, owing to the impracticability of setting up the instrument
+in a suitable position, sufficiently near to the pier to enable readings
+to be satisfactorily taken. This horizontal displacement probably
+amounted to about 1/16 inch either way. The rise and fall of the arches,
+and rocking either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect to the
+spans. Summarising the results, the greatest vertical movements
+downwards were 0·20 inch, 0·40 inch, and 0·22 inch for spans Nos. 1, 2,
+and 3, the upward movements being 0·08 inch and 0·13 inch for the first
+and second spans, there being no recorded result of this kind for the
+third span. With adjacent ribs loaded, the movement of the ribs unloaded
+was one from one-third to one-half of the full amounts. It is to be
+noted that the lateral displacement in no case exceeded 0·04 inch either
+way, nor were the vertical movements exceptional; yet, as a matter of
+sensation, when seated upon the ironwork, it was a little difficult to
+believe them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0·45 inch, 0·45 inch, and 0·55
+inch for the spans in order, the extreme temperatures being fairly
+representative of the English winter and summer. The structure was, as a
+consequence of the examination, efficiently braced by diaphragms between
+the ribs, and diagonals following the arch ribs round from springing to
+springing, with satisfactory results. The crack already referred to, and
+its probable causes, will be dealt with under “Cast-Iron Bridges.”
+Eventually this bridge was reconstructed to meet the requirements of
+growing engine-loads.
+
+
+
+
+CHAPTER VIII.
+
+DEFLECTIONS.
+
+
+Deflection, considered only as a fraction of the span, and without
+regard to other conditions affecting it, is of very little use as an
+indication of a girder’s fitness for its work; but when taken with
+reference to the depth of the girder, the nature and amount of the load
+producing flexure, and, further, with regard to the quality of the
+workmanship and normal properties of the material of which the beam is
+constructed, it may be of some little service in helping to form a
+reliable opinion. This consideration applies with less force, perhaps,
+to new work than to old, in which there may be unknown influences at
+work, or unknown defects which by excessive deflection may be betrayed.
+Though too much importance should not be attached to results of
+deflection tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each case, gives a
+good general idea of what may be expected in a fresh instance, any
+material departure from which should be a reason for specific inquiry as
+to the cause. A further reason with new work is found in the evidence it
+affords as to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case of floor
+beams, in what way the load is distributed amongst them, if, indeed,
+there be any such distribution.
+
+The author has commonly found that new work gives greater deflections
+than old--i.e., while calculation gives the same result for each, it
+does not apply equally well to both. The differences may be accidental,
+but are probably due to other causes, perhaps to the fact that new work
+has not by repeated applications of load lost the resilience of parts
+liable to considerable local stress, such as is very liable to occur at
+connections, so that the deflection is, whilst new, greater than after
+many years’ use, by which time such parts may develop a definite “set,”
+and contribute in a less degree, or not at all, to the total elastic
+deformation.
+
+It is also possible, as already suggested, that repeated high stress may
+reduce the ratio of strain to stress, the material gradually becoming
+more rigid, the modulus of elasticity being, in fact, increased.
+
+In girders of ordinary construction, the major part of the deflection is
+due to the booms, the remainder to the web; the latter is for plate
+girders a small amount only, and is commonly neglected, but for open web
+constructions it may be quite appreciable. For any given type of web
+arrangement the deflection due to the web will, for all depths, remain a
+constant quantity for the same span and unit stress; and though a
+moderate fraction of the whole deflection for a shallow girder, it may
+be a very considerable part for a girder of great depth, in which that
+part due to the booms is, of course, smaller, since the deflection due
+to these varies inversely as the girders’ depths.
+
+Deflection, being dependent upon the elasticity of the material, is of
+necessity very largely influenced by the value of its modulus E, itself
+liable to considerable variation, and is increased in a small degree by
+the yield of joints and rivets, which effect, apart from the initial
+“set” of the girders, appears to be negligible. The stiffness of members
+in resisting angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less, and,
+finally, section excess at joints and gusset attachments has an
+influence in modifying deflection as compared with that due to the
+normal gross sections simply.
+
+From these considerations it is apparent that any simple deflection
+formula must be largely empiric in its nature. For plate girders of
+uniform depth and flange stress, the writer has found the following to
+give good results:--
+
+   S^2
+  ----- × _f_ = deflection in inches.
+  D × C
+
+The span S and depth D are, as a matter of convenience, taken in feet;
+the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is
+the mean of the extreme tensile and compressive stresses of the booms,
+in tons per square inch, estimated upon the gross sections.
+
+This, though satisfactory for plate girders, is not so suited to girders
+having open webs, in which the deflection will more nearly be
+
+  (3S    S^2 )
+  (-- + -----) × _f_,
+  (C    D × C)
+
+the constant C being 3900 and 4450 for iron and steel respectively. The
+latter values of C correspond to normal values of the modulus of
+elasticity of 11,700 and 13,350 tons for iron and for steel, it being
+assumed that any slight rivet yield is off-set by any small section
+excess--say, 5 per cent.; it may, however, happen that section excess is
+greater than assumed, in which case some allowance may properly be made
+for this by increasing C.
+
+To adapt the formulæ to girders other than those having parallel booms
+and uniform stress, the results, as deduced above, may be multiplied by
+constants given in column B of the Table given on page 93.
+
+The practice of adopting for E in deflection formulæ a quantity much
+smaller than its nominal amount, with the object of allowing in riveted
+girder work for the yield of rivets and of joints, can hardly now be
+defended, whatever may have been a case at a time when workmanship was
+much inferior, when there was no machine riveting, and joints were,
+owing to the small weight of plates and bars, three times as numerous.
+
+The initial “set” of a girder consequent upon first loading is a
+quantity quite distinct from deflection proper, and may be so small as
+to be negligible, or read 10 per cent. of the true deflection, varying
+with design and workmanship.
+
+No estimate of girder deflection can be even approximately true if there
+is, at the level of the top or bottom flanges, a plated or otherwise
+rigid floor system which is not taken into account, as this will have
+the effect of very materially reducing the boom stress. To neglect this
+influence, where it exists, must necessarily lead to disappointing
+results, and it is quite practicable in many instances to include it in
+the calculation.
+
+The influence of angular distortion between the various members has been
+neglected. It may be pointed out, however, that the resistance
+accompanying these movements in girders having riveted connections,
+though unimportant as affecting deflection, is worth some consideration
+in regard to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount for any span,
+but will generally be of less importance in large girders than in small,
+because in large girders the ratio of the breadth of members to their
+length is commonly less.
+
+When determining the probable deflection of any girder of exceptional
+figure, it will be found convenient to make a strain diagram--an old
+device, in which the actual alterations of length being ascertained for
+all members, the girder is carefully set out to a suitable scale, with
+the lengths of members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the probable
+deflection. The value of E for this purpose should never be taken at
+less than the normal amount, and may for a considerable excess of metal
+in joints and gussets be made as much as 10 per cent. greater, this
+being a convenient means of making the necessary correction.
+
+The effect of loads quickly applied may here be considered in connection
+with elastic deformations of girders of the same span, but different
+depths. If these be designed for similar loads and unit stresses, the
+deflections due to webs and booms of the girders compared will bear the
+same relation, each to each, as do the weights, whether in both cases
+the loads be inert or quickly applied, from which it follows that the
+mechanical “work” done by the loads in falling through the deflection
+heights is, neglecting inertia, always in proportion to the girderwork
+weights, and is a similar amount per ton, which as the total length of
+members remains substantially unaltered, corresponds to a similar amount
+of work per unit of section, or similar stress, irrespective of the
+depth of the girders.
+
+But for a “drop” load, as when there is some obstruction upon a railway
+bridge, there will be in addition a further amount of work to be
+absorbed, which is to be considered the same whatever the girder’s
+depth, and will for deep girders be a larger amount per ton of
+girderwork than in those that are shallow; this, taking effect on
+members of the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in the booms.
+
+The influence of the girder’s inertia in modifying drop-load effects
+will also be less marked in deep--i.e., light--girders than in girders
+shallow and heavy.
+
+It is, notwithstanding all this, desirable that the depth of main
+girders should be liberal for economy’s sake, and also that of floor
+beams, for reasons already dealt with; the probability of the drop load
+is somewhat remote, and, though possible, would simply induce, if it
+occurred, an increment of stress rather more important in deep girders,
+making it specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact effects.
+
+It should be remarked that for short and very flexible beams, generally
+outside the limits of practice, there may also be, under quickly moving
+loads, a material increase of stress due to the centrifugal effort of
+the load on running round the deflection curve, and in rising upon the
+steep part of the curve beyond the girder’s centre. Where advisable,
+these effects may be modified by cambering the rail.
+
+For pin bridges in which there may be spring in the pins, excess stress
+in some eye-bars due to inequalities of length, and a want of that
+rigidity peculiar to riveted structures, the deflection will be greater
+than above indicated for girders of the ordinary English type.
+
+The method in common use for measuring the deflections of girders but a
+moderate distance above the ground by means of sliding-rods, though
+crude, gives, with care, results sufficiently accurate for most
+practical purposes; but some points necessary to remember may be
+mentioned with propriety. The lower rod should rest firmly upon
+something solid, say a stone, well bedded and free from any tendency to
+rock; the upper end should bear against some part of the girder above,
+presenting a hard surface, free from dirt or scale, and as the running
+load approaches the bridge it should be ascertained that there is no
+slack, that the rods bear hard at the top and bottom. The upper end
+having been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other. These
+precautions are so self-evident that an apology is almost necessary for
+mentioning them.
+
+To ascertain deflections with a single pair of rods is only allowable
+when the girders rest firmly on their bearings; if felt has been placed
+under the girder ends, or if the bedstones are insecure or rocking, it
+is necessary to use three pairs of rods, one pair at the middle and a
+pair at each end, in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the desired
+result.
+
+In the case of a number of spans in series, each resting upon sill
+girders common to two sets of bearings, this method also gives results
+of indifferent reliability, as the depression of each end may be greater
+as the travelling load comes upon and leaves the span than when it is
+precisely over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular position of
+the running load, which are what is required.
+
+The author suggests, as a means of ascertaining deflections free from
+these objections, that it should be done by first measuring the slope at
+one end, and from this deducing the deflection at the centre.
+
+This is to be accomplished by means of a little instrument, consisting
+of a telescope with cross-hair sights, and fitted with a reflecting
+prism at the eye-piece capable of being turned round, so that the
+observer has a wide choice as to the position he assumes with reference
+to the instrument, and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one end of the
+girder over the bearing, at the other end a scale is secured, to which
+the telescope is directed, the cross hair being made to sight on the
+zero of the scale, or the reading noted. For a girder supposed to
+deflect to uniform curvature (say, with uniform depth and uniform
+stress, the ordinary case) the reading observed will be four times the
+deflection; every 1/10 inch actual reading on the scale will correspond
+to 1/40 inch of girder deflection.
+
+Apart from the deflection, this method gives a ready means of observing
+the end slope, a quantity of equal value for purposes of comparison. As
+with girders of similar proportions, and similarly stressed, the
+deflection will at all spans be the same fraction of the span; so should
+the end slope be a constant quantity under similar conditions, the
+diagram, Fig. 54, will make the principle quite clear.
+
+[Illustration: FIGS. 54 to 57.]
+
+Strictly the character of the deflection curve is slightly modified by
+that part of the deflection due to the web; so that the depression at
+the centre would, in the case assumed above, be somewhat more than
+one-fourth part of the end reading, and generally will be a larger
+fraction of the reading than that deduced from a consideration of flange
+stress simply. In Figs. 55 to 57, which are intended to explain this,
+it will be noticed that deflection due to the web is shown
+straight-lined from the bearings to the centre of the girder; this is
+strictly true only for a girder correctly designed for an immovable
+distributed load; but as there should be for girders intended for a
+travelling load, some excess in web members near the centre under the
+condition of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as shown in the
+diagram for the sake of simplicity.
+
+Suitable constants, including the corrections necessary, are given in
+column A of the table annexed for a few typical cases, and by these
+constants the actual readings should be multiplied to find the
+deflection. The constants have been worked out for depths of one-tenth
+the span; for greater depths they should be slightly more, and for
+smaller depths somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly exceeding 5
+per cent., and generally much less.
+
+The figures in column B relate to the formulæ previously stated, and
+apply equally well to all depths.
+
+TABLES OF MULTIPLIERS FOR DEFLECTION.
+
+  _Uniform Stress_:                                           A.     B.
+      Girders of uniform depth, varying flange section       0·27   1·00
+      Hog-backed girders, ends half of centre depth, varying
+      flange section                                         0·24   1·08
+  _Varying Stress_:
+      [1]Girders of uniform depth and flange section         0·32   0·87
+      [1]Hog-backed girders (as above), but uniform flange
+      section                                                0·29   0·97
+      [1]Bow-string girders of uniform flange section        0·16   1·30
+
+[Footnote 1: For uniform loading.]
+
+It is apparent that, if preferred, the scale, instead of being in
+inches, divided suitably, may, for each type of girder, be amplified to
+the proper degree, so that the amount of the deflection may be read off
+at once.
+
+This method of dealing with deflections is quite independent of the
+character of the bearings, and is applicable to girders at any height
+above ground or over water; but its use would hardly be practicable for
+very small beams, or those in an awkward position, or near which it
+would be impossible to remain with a running load upon the bridge.
+
+There is a possible source of error in the use of the instrument, most
+likely to occur with triangulated girders, with which, if the instrument
+is placed at the top of an end post, the reading observed may be the
+joint effect of deflection and of local flexure of the members meeting
+near the telescope. This may be tested, and, if necessary, allowed for,
+by first sighting upon a scale at the next apex, and observing the
+effect of the moving load. Again, as girders sometimes cant towards the
+running load, if the instrument is placed on one edge of a girder, and
+the cantings of the two ends are dissimilar, a false reading will
+result, which may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between the cants
+upon the observation. Only in exceptional cases is it likely that either
+of these considerations would need attention.
+
+The author has secured with this instrument very promising results,
+notwithstanding that under a running load there is a slight haziness of
+the scale as seen through the telescope, due to “dither,” largely the
+result of imperfections which may be remedied.
+
+Deflections may sometimes be conveniently taken, by a quick-eyed
+observer, with a good surveyor’s level and a specially-divided staff
+held at the centre of the girder. The divisions preferred by the author
+for this purpose are 1/10 inch, plainly marked, which may be seen at 50
+feet distance with sufficient clearness to make possible readings by
+estimation between the divisions to, say, 1/50 inch. But it is clearly
+desirable not to rely upon a single observation only, where all the
+evidence is gone so soon as the sight has been taken.
+
+In rail-bearers, or other short girders, it may not be practicable to
+adopt such methods, either on account of an inability to find a suitable
+place for the instrument, or to read with any telescope with sufficient
+promptitude as the load passes rapidly over. The use of rods may also be
+out of the question, as the errors attending their manipulation may be
+serious where but a small movement has to be noted, this being
+complicated in some instances by the bearings being insecure, and
+working to an extent which obscures the measurement sought. In such
+cases it is preferable to use a stiff slat lying along the girder, which
+bears, through short blocks over the girder bearings, upon the flanges;
+the deflection is then read by direct measurement of the girder’s
+depression at the centre, relative to the slat.
+
+The author is, unfortunately, not able to give any precise information
+on the effect of running-load as against a load that is stationary in
+connection with girder deflections. It is by no means easy in ordinary
+work upon a railway to secure facilities for making such comparative
+tests. It may, however, be confidently stated, as a result of such
+observations as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a 50 feet
+span, but little greater than that due to the same load stationary; it
+may be, perhaps, 5 to 10 per cent. more.
+
+It is evident that to determine the precise difference where the
+quantity to be measured is so small needs apparatus of a more delicate
+character than that in common use, and the control of an engine, or
+engines, for the purpose of making the special tests, conditions which
+on a busy line can only be secured by special arrangements previously
+made.
+
+
+
+
+CHAPTER IX.
+
+DECAY AND PAINTING.
+
+
+The author has collected particulars as to the amount and rate of
+rusting in metallic structures which are of some interest. In all such
+instances it is very necessary to note the conditions which have
+obtained during the process of wasting, as without this, misleading
+conclusions may be drawn. The information given relates in all cases to
+wrought iron, unless otherwise stated.
+
+A plate-girder bridge, having girders under rails, was found to be badly
+rusted. The atmospheric conditions were unusually trying, the air being
+damp and impregnated with acid fumes from adjacent steel works. That the
+wasting was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than those
+farther removed and partly sheltered from the corrosive influence.
+
+The webs were in places eaten right through, having lost a mean amount
+of about 1/8 inch full on each surface in twenty-eight years. Painting
+had not been well attended to.
+
+In a similar bridge, not a great distance from this, but sufficiently
+far away to modify the conditions for the better, considerable wasting
+was also observed, but more particularly where the girders had been
+built into masonry, which, loosening with the constant movement of the
+girder-ends, had allowed moisture to collect, and rust to develop,
+without the chance of repainting these surfaces. The amount of waste at
+the places indicated was, as in the last case, about 1/8 inch on each
+face, and in the same time, other parts of the girders having suffered
+less.
+
+[Illustration: FIG. 58.]
+
+A third plate-girder bridge, with outer main girders, cross-girders, and
+plated floor, carrying a road over a railway and sidings, and which was
+known to have been neglected in the matter of painting, was very badly
+rusted, both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration was, however, the
+smoke and steam from locomotives, which frequently stood for some time,
+during shunting operations, directly under the bridge. The webs of the
+cross-girders, which were originally 1/4 inch thick, had rusted into
+occasional holes during fourteen years--i.e. 1/8 inch from each surface
+in that time. When removed a little later the wasting was so complete
+that it was possible to knock out with a light hammer the remains of the
+web between flanges and stiffeners, so as to leave an open frame only.
+One of the cross-girders was so treated by the men engaged upon the
+work, when it presented the appearance shown in Fig. 58.
+
+In another case--that of a bridge with lattice girders under rails--the
+ends were built into masonry, which had, of course, loosened, with the
+usual result. The air of the locality was certainly pure, but somewhat
+damp. The general condition of the ironwork was good, but end-bars of
+the diagonal bracing, where they had been closed in, had lost 1/8 inch
+on each surface in thirty-three years. The top flanges immediately under
+the timber floor were in a very fair state, which is of some interest
+when it is considered that these were made of steel of the same kind as
+that already noticed as being used in the construction of small girders
+(see Fig. 46, _ante_), described in the chapter upon “High Stress,” both
+cases dating from the year 1861. The painting upon the lattice-girder
+bridge had been pretty well attended to; but in the case of the small
+steel girders it had been greatly--perhaps altogether--neglected; this,
+coupled with adverse atmospheric conditions, had produced the result
+that the rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully 1/8 inch on
+each surface, as against a negligible amount under the more favourable
+circumstances.
+
+Girder-work over sea-water, as in piers, seems to rust at a sensibly
+greater rate than inland work under average conditions; but it is hardly
+practicable to make any strict comparison, as in either case the rate of
+oxidation is so much affected--even controlled--by the care bestowed
+upon the structures. This general conclusion is based upon the results
+of examination of wrought-iron girder-work over sea-water of ages
+varying from fourteen to forty-four years. It should be remarked,
+however, that in one case steel girders but five years old, and which
+were frequently wetted with sea-spray, were found to be wasting rather
+badly--the paint refusing to keep upon the surface.
+
+It may be concluded from the above instances, and from others which have
+come under notice, that wrought-iron work, if not properly cared for in
+respect to painting, or under conditions otherwise bad, may be expected
+to rust at a rate which corresponds to the loss of 1/8 inch on each
+surface in from fifteen to thirty years; but with proper care as to
+painting, and exclusive of exceptionally bad conditions, it does not
+appear to waste at any measurable rate. In some instances, upon scraping
+the paint from girders which had been in use for thirty years, the
+author has found, beneath the original red lead, the metallic surface
+bright and clean, showing no trace of rust.
+
+Of ordinary steelwork the same cannot be said, the common experience
+being that mild steel is very liable to be attacked by rust. With
+passable care in the bridge-yard during manufacture, such that with
+wrought iron no after-trouble would be noticeable, steel is very liable
+to show, within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away discloses a
+small rust-pit. This is more often seen on the flange surfaces
+(horizontal) than on web surfaces (vertical), but it is probable the
+position has little to do with the matter, and that it is rather due to
+the fact that rust has been earlier started on the flange-plates, upon
+being put through the drilling-machines and inundated with slurry, which
+occurs only to a more limited extent with webs having fewer holes. The
+heads of steel rivets do not show this tendency to “pit,” or to early
+development of rust. The riveting is about the last operation in making
+a girder, each rivet being freed of all rust by heating, and quickly
+coming under the protection of oil or paint. It may happen in this way
+that the heads of rivets on a girder may be exposed without protection
+for as many hours only as the rest of the work for weeks, which fully
+accounts for the difference in behaviour.
+
+The essential point to be observed in all steelwork is to prevent, if
+possible, the first development of rust, for once begun it is much more
+difficult to arrest than in iron; for this reason, oiling of all
+material for a steel bridge, at a very early stage of its existence,
+cannot be too strongly insisted upon. This practice, however, makes the
+work so objectionable, and even dangerous when being lifted--because of
+the liability to slip--to the men engaged upon it, that it is commonly
+very difficult to ensure it being done sufficiently soon to satisfy a
+careful inspector. If the work is carried out under cover, the
+requirement is less urgent. Strictly, all material should be oiled so
+soon as rolled, but the author does not remember to have seen this done
+at any of the mills he has visited, though it is common enough to find
+it specified.
+
+Ironwork does not need the extreme care which should be bestowed upon
+steelwork, but it is desirable that it should be painted as soon as
+possible, the surfaces being first thoroughly cleaned.
+
+There is, probably, for painting girder work nothing to beat good red
+lead as a protective coating; but there is considerable difficulty in
+getting it reasonably pure, without which quality its utility will be
+greatly reduced. The question of purity will, however, be found to be
+largely a question of price. It may be stated broadly that, whether for
+steel or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.
+
+In repainting old work, care should be taken to remove all traces of
+rust previous to laying on the new coat. It is not an altogether
+uncommon practice to repaint old structures by dealing only with the
+parts readily accessible, which, being less liable to rust, probably but
+little need it; leaving those parts which are difficult of access, and
+where rust is developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said, is
+indefensible. It is better rather to neglect the surfaces freely exposed
+and ventilated, and devote the whole care upon those other parts,
+confined and difficult to get at; taking the trouble necessary to remove
+ballast, timber, or whatever may obstruct the operation, in order that
+the bad places may be thoroughly scraped, and then painted. Those parts
+which most need attention may cost, perhaps, to reach--and deal with
+when exposed--ten times as much per yard of surface as the rest of the
+superfices, which needs little, and is always accessible; but the cost
+should not deter the proper carrying out of the work, as it will prove
+the very worst sort of economy to deal with painting in a perfunctory
+manner.
+
+It should be noted that girder work, whether of wrought or cast iron,
+when embedded in lime or cement concrete, or mortar, generally proves to
+be very well preserved, provided that close contact has obtained.
+Cast-iron girders, when carrying jack arches resting upon the bottom
+flanges, are found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of new
+girders. Much the same remarks apply to girders of wrought iron carrying
+jack arches, where protected by the brickwork; provided that the girders
+are sufficiently stiff to minimise deflection, and allow the masonry or
+brickwork to adhere to the surfaces.
+
+Such girders are in a very different condition to those previously
+referred to, in which the ends of the girders, carrying a light floor
+structure, are built into masonry where the deflection slope is
+greatest; though, apart from the few cases where adherence can be relied
+upon, building-in is an undesirable practice, and has the disadvantage
+that after-examination is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted to.
+
+Cast iron has ordinarily--unlike wrought iron or steel--great capacity
+for resisting rust, and will, after many years of absolute neglect,
+appear but little the worse; an advantage which is the more pronounced
+when considered relatively to the greater thickness of the thinnest
+parts in cast-iron girders, the percentage of waste being
+proportionately lessened.
+
+Cast iron does, however, behave somewhat badly in sea-water, the metal
+sometimes losing its original character, and becoming in time quite
+soft; though, if not worn away, as by the attrition of shingle,
+maintaining its original bulk.
+
+Of some forty-five cast-iron piles belonging to various structures,
+examined whilst engaged upon sea-pier work for Mr. St. George-Moore,
+though the author found somewhat diverse results, in no case did there
+appear to be any general softening of the whole thickness, but a
+distinct change for some definite distance inwards, generally to be
+decided without difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of softening was
+found close to the ground, this depth rapidly decreasing higher up,
+till, at a height of 5 feet, but little if any softening could be
+detected. At 2 feet above ground the softening was frequently but
+one-quarter of that at ground level. There was, too, often a
+considerable difference in the behaviour of different piles in the same
+structure under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly none at
+all. For six different structures the amount of softening near ground
+level, of about twenty-five piles examined, was as given in the table on
+the next page.
+
+The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot
+above ground, in a pile thirty-six years old. The decayed material when
+removed was of a soft, greasy consistency, perfectly black, which a few
+hours later was found to have changed to a dry yellow powder, by the
+rapid absorption, it may be supposed, of atmospheric oxygen. It is
+apparent, therefore, from this example that deterioration may proceed to
+a considerable depth; but it should be observed that other piles of the
+set showed softening at ground level of 1/8 inch only.
+
+SOFTENING OF CAST-IRON PILES IN SEA-WATER.
+
+  ---+--------+----------+-----------+----------+---------+---------
+  No.|  Age.  | Maximum  |  Maximum  |Mean Rate | Quality |Materials
+     |        |Softening.|  Rate of  |    of    |of Metal.|Entered
+     |        |          |Softening. |Softening.|         |by Piles.
+  ---+--------+----------+-----------+----------+---------+---------
+  1  |17 years|5/16 in.  |1/8 in. in |1/8 in. in|Soft     |Extremely
+     |        |          |7 years    |15  years |         |soft
+     |        |          |           |          |         |sandstone.
+  2  |36 years|9/16  „   |1/8 in. in |No result |  „      |Rubble
+     |        |          |8-1/2 years|          |         |mound.
+  3  |32 years|3/8   „   |1/8 in. in |1/8 in. in|Moderate-|Fine
+     |        |          |11 years   |15  years |ly hard  |sand.
+  4  |38 years|1/10  „   |1/8 in. in |1/8 in. in|Hard     |Extremely
+     |        |          |47 years   |140 years |         |hard rock.
+  5  |17 years|Small     |Negligible |          |(?)      |Sand and
+     |        |          |           |          |         |Shingle.
+  6  |14 years|Negligible|Ditto      |          |(?)      |Sand.
+  ---+--------+----------+-----------+----------+---------+----------
+
+The least rate of softening noticed, apart from those structures of a
+more recent date, in two of which it was very slight, occurred in a
+pier thirty-eight years old (No. 4), where, of three piles tested, two
+were quite hard, and the third softened 1/10 inch only.
+
+Whatever may be the precise cause of the change, it does not appear to
+be affected by the period or percentage of immersion during the rise and
+fall of tides.
+
+[Illustration: FIG. 59.]
+
+This will be clear from the diagram, Fig. 59, which refers to four piles
+(No. 3 of table), all of the same age, in the same structure. On each
+pile the depth of softening is given at points in strict relation to
+each other, and to the tidal range. The percentages of immersion for the
+various heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening; this,
+indeed, is always greatest near the ground, at whatever actual height it
+may be. For instance, pile A was at ground-level softened 1/4 inch,
+that point being 60 per cent. of its life under water; but on pile B, at
+a point 74 per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level of
+this pile, the percentage being there 87, the softening was no greater
+than at ground-level at pile A.
+
+It is probable that while the percentage of submersion in moving water
+hardly appears to affect the result, yet prolonged contact with wet
+sand, sea-weed, or clinging shell-fish may do so. This seems to suggest
+that the process of change, as between the sea-water and the iron, is
+slow, and to be effective must be continuous; so that it is only found
+to any considerable extent where the water in contact with the surface
+is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1
+foot and 6 inches above ground-level, the surface was in one pile
+shrouded in a thick mantle of heavy sea-weed, and in the other covered
+by molluscs; in both instances the surfaces being thus kept moist and
+undisturbed. The piles of the fourth case were in hard rock, were clean,
+and, where accessible, always either in moving water or quite dry.
+
+However this may be, the power to resist softening certainly appears to
+vary largely with the quality of the iron. The piles, referred to above,
+in which deterioration proceeded at the most rapid rate were certainly
+of a soft metal, the first being markedly so. On the other hand, certain
+piles (No. 4) of hard, close-grained iron suffered very little.
+
+It may be mentioned with respect to the last named, as a matter of
+interest, that the caps of the lower lengths (just above ground-level)
+had been cast with short pieces of wrought iron projecting--possibly for
+lifting purposes--which during thirty-eight years had altered in
+character to something very like softened cast iron, but laminated, and
+harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained
+having the semblance of wrought iron. The percentage of submersion was
+about 60.
+
+A number of piles, not included in the table, varying from fifteen to
+forty-four years old, and of the same structure to which set No. 2
+belonged, were all found to be hard, with the exception of one showing
+3/16 inch of softening. These are omitted, because the mud surrounding
+them was at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points testing might
+have disclosed different results. It is probable that for any piles
+standing in soft material examination below the surface would reveal
+more pronounced softening than where occasionally exposed.
+
+To meet the effects of sea-water on cast-iron piles, and for other
+reasons, it is a common and good practice to make the lower lengths of
+greater thickness--say, 3/8 inch more--than that sufficient for the
+upper. Occasionally, also, the bottom lengths are filled with concrete,
+which no doubt adds to the length of time during which they may be
+relied upon.
+
+
+
+
+CHAPTER X.
+
+EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+
+In the preceding chapters defects of various kinds to which riveted
+bridgework is liable have been more particularly dealt with; it is now
+proposed to consider the examination of such structures, following this
+by a reference to methods of repair and strengthening, leaving the
+treatment of other classes of bridgework to be developed under their
+proper headings, though some of the remarks immediately following will
+apply to all.
+
+The exhaustive survey of a bridge is only to be made after considerable
+experience in the work, but it may be stated that in looking for defects
+it is well to seek where they are least expected, till, with practice,
+one knows better where to direct attention. When examining with a view
+to pronouncing an opinion upon the fitness of the structure to remain in
+place, if in any real doubt, it is wise to give a casting vote against
+it; and finally it may be said that upon taking down a bridge condemned
+for any one or more defects, it should be examined for worse. This may
+seem to be somewhat pessimistic, but is based upon the teachings of
+experience.
+
+Preliminary examination of a bridge may reveal such faults or weaknesses
+as at once to ensure its condemnation; but if this is not the case, and
+there is a reasonable probability that the structure may be given a
+fresh lease of life, it will, for the purpose of estimating the
+strength, or for possible repairs, commonly be desirable to secure
+precise particulars of the existing structure independently of any
+drawings that may be in existence, and which will very probably be
+incorrect, the finished work, if old, seldom agreeing with the contract
+drawings. A final decision may in this case be deferred till after the
+measuring up has been completed, the condition of the structure becoming
+more familiar in the process.
+
+It is desirable first to ascertain whether the bridge remains in good
+form, whether the camber of girders appears to be what might be
+expected, or agreeable with existing records, though much reliance must
+not be placed upon figured cambers, it being quite common for girders to
+leave the bridge yards with the camber something other than that
+intended. The deflections under live load will also be observed, and
+compared with the calculated result, or checked by judgment. The
+calculations upon which strength and deflections are based will, of
+course, refer to the actual sections, which are sometimes a little
+difficult to ascertain if there has been irregular rusting. In
+continuous girders also, levels having been taken, allowance should be
+made for effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the like object. It
+is seldom that the main flanges of girders show signs of weakness,
+unless from flexure in the case of long and narrow top members,
+insufficiently stiffened; but there may be want of truth from other
+causes already dealt with. In plate girders the webs should be most
+carefully scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange angles, if the
+floor rest upon the flange. All riveted connections, of course, need
+close attention, both for straining effects, where there is a liability
+to wracking, and to detect loose rivets. Loose rivets and want of
+tightness in other parts of the work may frequently be detected at
+sight by a reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects of weather;
+it may be seen round rivet-heads or along the edges of angle-bars, or
+other parts where there is movement. Loose rivets, though generally to
+be detected also by the hammer, may perhaps in the case of thin-webbed
+cross-girders be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may sometimes be
+detected by simultaneous deflection tests--with rods--at the top and
+bottom flanges of a girder, at the same distance from the bearings. Any
+difference in the readings may indicate loose web-rivets, or possibly a
+tear in the web running parallel to the flange angles.
+
+Bracings between girders are very apt to display a rich harvest of
+working rivets. Cross-girders and longitudinals also may have loose
+rivets at their connections, and be very badly wasted, with quite
+possibly cracks in the webs, or other defects already enlarged upon.
+
+The condition of the road upon the bridge will frequently be an
+indication of the state of the floor which carries it; or the existence
+of rail-joints which are working badly may very properly lead to a
+critical examination of the girder-work immediately below, as this is a
+fruitful source of damage in light constructions. Floor-plates, where
+these exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the latter
+being often loose and unsatisfactory.
+
+Trough floors may be expected to show loose rivets near the ends, with a
+probability of excessive leakage where they abut against the webs of
+supporting girders.
+
+Floor plates resting upon abutments or piers, being very liable to
+serious decay, require attention, and girder-work entering masonry
+should receive close scrutiny, any obstruction to a sufficient
+examination being removed so far as is judged sufficient for the
+purpose. The structure should, of course, be closely watched during the
+passage of live load for any signs of abnormal movement, excessive
+vibration, or lurching.
+
+In addition to seeking for these various defects, or others which have
+been referred to in these pages at length, it will be well always to be
+alive to the possibility of faults to be seen for the first time, or of
+which the author has furnished no instance.
+
+Having formed a reliable opinion as to the state of the bridge, this, if
+satisfactory, may leave to be determined only the question of strength
+relative to the loads carried. It is apparent that stress limits
+suitable for a new structure, which has all its life before it, of
+purpose moderate to cover possible deteriorations, the growth of loads,
+and other adverse influences, may to avoid immediate reconstruction,
+reasonably be permitted of a higher value for a further term of years in
+the case of a structure which it is known has for a considerable period
+behaved well, and remains in good condition. What this higher value may
+be will be greatly influenced by the circumstances of each case, and,
+being largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the nominal unit
+stress in an old bridge may be a very considerable amount in excess of
+that allowed for new work, without, of necessity, showing any ill
+effects; and the author is of opinion that for old bridges in good
+condition it is quite prudent to allow an excess of 33 per cent. beyond
+that permissible for a new design. If the structure is too weak to
+satisfy this modified condition, it may be possible to bring it within
+the stress limit by a reduction of ballast or other removable dead
+weight. If this expedient does not promise to be satisfactory, or the
+bridge shows actual signs of weakness, or palpable defects, it will be
+necessary to deal with the question of repair, strengthening, or
+reconstruction.
+
+The repair of built up bridgework resolves itself largely into a matter
+of replacing loose rivets by cutting these out, rhymering the holes, if
+desirable, and again riveting. It will often be sufficient to do this
+with no particular precautions as to bolting up temporarily; the rivets
+having been loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to remove all
+the rivets, bolting up securely as this is done, in order to make a
+tight job, taking out each bolt in turn as required, and again filling
+the holes; or it may be well in a bad case first to remove all loose
+rivets, substituting good bolts, in order that work which has gone out
+of shape owing to defective rivets may first be brought true.
+
+Cross-girder webs, cracked vertically or nearly so, are commonly
+repaired with splice-plates on either side; but in doing this it is
+undesirable to add plates of excessive thickness relative to the
+web--probably poor--as by an abrupt change of web section it appears not
+unlikely a fresh break may be favoured.
+
+[Illustration: FIG. 60.]
+
+[Illustration: FIG. 61.]
+
+[Illustration: FIG. 62.]
+
+[Illustration: FIG. 63.]
+
+Replacing wasted flange-plates, or adding new plates to those which
+exist, is occasionally resorted to in the case of main girders, the
+flanges of which are sufficiently accessible, but the operation is
+difficult, takes some little time, and should only be attempted under
+the constant supervision of a thoroughly capable man. When done, if the
+girder has not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the new section,
+the old always taking more by the amount of the dead-load stress
+previously carried. The method which the author has seen applied to
+lattice girders of about 80 feet span, having good angle-bars in the
+flanges, with a shallow vertical web for attachment of diagonals,
+consisted in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been removed.
+The new plate length having been prepared, was, on a Sunday, during a
+few hours’ cessation of traffic, marked off, the temporary bolts being
+removed for the purpose, and then replaced. After the plate had been
+drilled, on a later Sunday, it was finally put into position, bolted up,
+and riveted at leisure; cover-plates make additional trouble, but are
+dealt with on the same principle. The method as shown in Fig. 60 is,
+however, barely practicable for so many plates. It is preferable, if it
+is proposed to add section, to do this with as little interference as
+possible with existing rivets of importance. This may be accomplished,
+if the existing plates are not too wasted at their edges, by riveting on
+new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength
+of a girder is increased by the addition to the top or bottom boom of
+material in such a form as sensibly to increase the depth, and thus,
+while adding increased section to one boom, to reduce the stress in
+each, though to dissimilar amounts. By this device also the relief is
+effective only as regards the live-load stress; under dead load only the
+new material does no work, provided, of course, that no relief staging
+was used during the alterations. For girders carrying any considerable
+proportion of dead load the method is very inefficient, though for
+others, in which the live load is relatively large, the result should be
+more satisfactory.
+
+As this question of adding new section to old is of much importance in
+dealing with repairs and strengthening operations, a few general remarks
+upon the subject will be pertinent. The difficulty in such work commonly
+is to cause the new to render any considerable assistance to the old in
+those cases which occur in practice. If a bar be imagined under
+longitudinal stress varying between 0 and a maximum, then, if the area
+of the piece be increased at the time when it takes no stress, its
+capacity for resisting the maximum amount will be increased, and for
+added material of similar elasticity the unit stress proportionately
+reduced. If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any degree.
+To take a third case, of the maximum being twice the minimum load, it
+will be necessary, in order to lower the maximum unit stress by 25 per
+cent., to double the original section of the bar if, as supposed, the
+extra metal has been added to the piece when under the smaller load, so
+that the new section is only effective in assisting to carry the
+remainder of the load at such times as it may be imposed. The
+relationship stands thus:--
+
+      Live load         New area
+  ---------------- × -------------- = relief.
+  Live + dead load   New + old area
+
+These statements will be true under the conditions named, within the
+elastic limit of the material; but some advantage would be derived in
+the second case, and a more marked benefit in the third, if the load
+assumed to be a maximum were exceeded, or if the composite bar were
+tested to destruction; as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment as to how
+far this reserve of strength may be considered of value.
+
+If, instead of simply adding section to the bar, some part of the
+constant load is put upon the new section by the manner of attachment,
+the combination will, of course, be more effective.
+
+To apply these considerations and illustrate the way in which the two
+methods of adding flange section work out when reduced to figures, the
+case will be supposed of a girder 6 feet deep, carrying a load of which
+one-third is dead and two-thirds live. To the flanges of this girder are
+added plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the girder before
+strengthening is liable, the depth remaining substantially unaltered.
+With dead load only the original section would be stressed to 2·3 tons
+per square inch, the new section being then unstressed. Under full load
+the new and old material take 3·1 tons per square inch additional,
+making the modified stress on the original section 5·4 tons per square
+inch, as against 7 tons; or a reduction of 22 per cent. This compares
+with 33 per cent., the relief due to 50 per cent. increase of flange
+area under ordinary conditions of stress distribution.
+
+Let the second method of strengthening the girder now be considered,
+using, for purposes of comparison, the same total amount of new material
+to increase the girder depth by an addition to the top flange. This
+section will be equal to the area of one flange, which, though it may
+be applied in many different ways, giving a greater or a less increase
+to the depth, would probably be used in some such manner as that shown
+in Fig. 64, increasing the effective depth for live-load stress by
+nearly 10 inches.
+
+[Illustration: FIG. 64.]
+
+The added material will, as in the previous case, leave the dead-load
+stress unaltered, or 2·3 tons per square inch. The stress in the bottom
+flange due to live load will, however, now be 4·1 tons per square inch,
+making a total stress of 6·4 tons per square inch, against 7 tons--the
+original stress. The reduction here is 8 per cent. only, as compared
+with 12 per cent., the relief due, under ordinary conditions, to an
+increase of effective depth from 6 feet to 6 feet 10 inches, and by the
+use of additional material, equal, as before, to one-half of the total
+flange areas before the alteration.
+
+The effect on the top flange need not be here gone into in detail, but
+it may be said that, owing to the increase of gross section and of
+depth, the ultimate stresses of both the new and old material are
+greatly less than as given for the bottom flange.
+
+Girders strengthened by the first of these two methods would, it is
+probable, if tested to destruction, give results more nearly in accord
+with the actual percentage increase of flange section, plastic
+deformation of the metal, before failure, tending to reduce the
+differences of stress on the new and old material of the sections.
+
+[Illustration: FIGS. 65 and 66.]
+
+Web members of lattice girders may, if weak, sometimes be dealt with by
+the introduction of supplementary bars, parallel to and between the old
+members, or by the addition of strips or angles to the existing
+diagonals. The treatment will be largely influenced by the nature of the
+old detail, which may lend itself to some one arrangement much better
+than to any other.
+
+End riveting of web members may, if it has become loose, be dealt with
+by simply rhymering the holes a size larger, and re-riveting in the best
+manner, if the stresses are not excessive; or it may be necessary to
+devise some additional attachments by which new rivets are brought into
+use (see Figs. 65 and 66). The effective relief due to supplementary
+rivets will be influenced by similar considerations to those governing
+increase of section.
+
+[Illustration: FIG. 67.]
+
+[Illustration: FIG. 68.]
+
+Old structures are very frequently deficient in bracing, which may, in
+such cases, be advantageously introduced; or girders individually weak
+may be rendered collectively efficient by suitable bracing. In
+considering the advisability of this, however, the case should be viewed
+with regard to the possible effects of such members, as already dealt
+with in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders may have
+the effect, under live load, of increasing the stress on the outer
+girders due to twisting of the structure as a whole, though the inner
+girders will, except for full loading of the whole bridge, be advantaged
+as to stress values, and in any event bettered by being held up to their
+work. The effect upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations the
+detail should be schemed with special care to ensure simplicity in
+execution, smith’s work being rigorously avoided. A good arrangement for
+supplementary bracing between plate-girders, which gives little trouble
+in carrying out, is shown in Fig. 67; or where the stiffeners of such
+girders are in line across the bridge, the detail given in Fig. 68 may
+involve less expenditure. Difficulties may be experienced in riveting,
+unless great care is taken in the positioning of rivets. Fitting-bolts
+are only to be relied upon as such, if they really justify the name;
+they are, though easy to specify, by no means easy to secure under the
+conditions of practical work. Weak cross-girders may make
+alterations--in some cases considerable--necessary, to rectify the
+defect of strength. The removal of old girders to make room for new is
+seldom resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders between the
+old in cases where there is no plated floor to make the work difficult.
+By this method there is, of course, an increase of appreciable amount in
+the dead load carried by the main girders, which would in many instances
+be objectionable. With deep and heavy main girders, having plate webs,
+cross-girders may be strengthened by improving the end connections by
+suitable gussets, and attachment to good vertical stiffeners, the fixity
+of the ends thus aimed at being assured by overhead struts or girders,
+from one main girder to its fellow, at intervals apart well considered
+with reference to the horizontal strength of the top flanges, the whole
+thus making a closed frame, as shown in Fig. 69. The method appears
+feasible, but it should be stated that the author has not known it to be
+applied in its entirety as a means of strengthening an old floor.
+
+[Illustration: FIG. 69.]
+
+A simple and very common device consists in substituting for the
+ordinary cross-sleeper road, where this exists, stout timber
+longitudinals under the rails, which have, where the cross-girders do
+not exceed 5 feet centres, a marked distributive effect, tending to
+reduce the maximum load upon any individual girder. With a similar
+object, trough girders containing longitudinal timbers are sometimes
+adopted where the depth available is not enough to enable sufficiently
+stiff timbers to be used alone. In either case the object sought is the
+same--to modify the effect of the heavier wheel loads upon isolated
+cross-girders. When the spacing is so close as 4 feet, the beneficial
+result of this treatment is considerable, but at 8 feet centres it can
+have but a moderate effect where timbers alone are used.
+
+Occasionally, for long cross-girders, a distributing girder is placed,
+with the same intent, in the 6 feet way, its function being limited to
+this use only if the depth and strength are sufficiently small to serve
+this object alone, as distinct from the case in which it becomes a
+carrying girder transferring load to the abutments. As a distributor
+simply, the girder has to equalise the bending moments amongst the
+cross-girders, to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous to
+alteration, for a position of the wheel loads such that the heaviest
+comes upon a centre cross-girder, the mean of these moments will, when
+compared with that for each girder, show the difference to be induced as
+a result of introducing the distributor. These differences of moment
+render necessary at the centre of the cross-girders reactions upwards or
+downwards, as the case may be, of amounts competent to induce moments
+below the inner rails equal to these differences.
+
+It is these reactions which must be provided by the distributing girder
+at a moderate stress, and without flexure of such an amount as sensibly
+to modify the reactions. The greatest section necessary at any one point
+may then be adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no harm in a little
+excess in a case of this kind, the total cost being but little affected
+by some small addition to the weight, where labour upon the site is so
+considerable an item as in work of this description. The ends of the
+distributing girder should be carried on to the abutments or piers to
+ensure adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at an early
+stage, by boning or by levelling, the condition of the cross-girders as
+to uniformity of heights, as this may affect the length most suitable
+for separate sections. Between the underside of the distributor and the
+cross-girder tops there will commonly be spaces of varying amounts,
+which should be filled by packings to fit, rather than by pulling the
+work together by force, introducing undesirable stresses of uncertain
+amount.
+
+In the earlier remarks upon the strengthening of bridgework by the use
+of new material, it has been assumed that the modulus of elasticity of
+the new metal is similar to that of the old; it may, however, as in
+cases where wrought-iron work is reinforced by additions in steel, be
+necessary to take the difference of elastic properties into account,
+with which object the new section should be multiplied by a quantity
+(greater or less than unity) inversely proportional to the higher or
+lower modulus of the new material, that is to say, by
+
+  E of old material
+  -----------------
+  E of new material
+
+
+
+
+CHAPTER XI.
+
+STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+
+The addition of distributing girders, described in the last chapter, as
+a means of strengthening a bridge floor, while sufficient in many cases
+so far as the cross-girders are concerned, does not in any appreciable
+way assist the main girders. When for a two-line bridge, having outer
+main girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders may be used,
+placed either above or below the cross-girders, on the centre line of
+the bridge.
+
+There are two principal ways in which such a girder may be brought into
+use; the easier, but generally less economical, is by making a simple
+attachment to the cross-girders, the old girder work still taking the
+whole dead load. By this method the new girder does no work but carry
+itself till the live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the second
+method is to make the connection adjustable, so that a part of the floor
+weights may be imposed upon the new girder as an initial load. In doing
+this the old outer girders will rise slightly, being relieved of stress,
+and the cross-girders also lifted at the middle, whilst the new girder
+is depressed as the load is brought upon it. With some part of the live
+load a very considerable proportion of the total may in this way be
+carried by a centre girder of moderate section. The whole question, by
+either method, turns upon deflections; and it is in determining the
+relative movements of the girders that the problem chiefly lies.
+
+It is convenient first to determine the percentage of load relief to be
+effected in the main girders, as to which it is to be observed that as
+this relief (distributed) is induced by the upward reaction of the new
+girder acting at the centre of the cross-girders, the stress relief of
+these will, as a rule, greatly exceed that of the outside girders. For
+the generality of cases, it may be taken that the relief suitable for
+the outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress in these
+to a greater degree.
+
+If, however, it be thought desirable to check this, it may be done by
+considering a cross-girder subject to its dead and live loads acting
+downwards, and to reactions at the centre and ends. At the centre the
+reaction will be the load of which the two main girders are relieved on
+a length equal to the pitch of the cross-girders, or as here given:--
+
+  _c_ × _t_ × P = reaction at centre (1)
+
+_c_ being the percentage of relief; _t_ the total load per foot run of
+the bridge; and P the pitch of cross-girders. The live loads carried by
+the cross-girders are for this purpose taken at per foot run, as for the
+main girders. With these data it will be easy to construct a diagram of
+moments, making it evident whether the relief proposed for the main
+girders will give a sufficient percentage of relief to the floor beams.
+
+Granting that this proportion has been decided, and dealing first with
+the case in which the centre girder is simply attached to the
+cross-girders, and takes no dead load other than its own weight, then
+the live load carried by the outside girders, and previously borne
+wholly by them, will be reduced by the amount it is intended to transfer
+to the centre girder, and will become
+
+  L{_l_} - (_c_ × L{_t_}) = live load on outer girders (2)
+
+L{_l_} being the total live load, and L{_t_} the total dead and live
+load carried by the bridge. From this the deflection of the outer
+girders corresponding to this modified live load may be derived.
+
+[Illustration: FIG. 70.]
+
+It is next necessary to ascertain the vertical movement, commonly a
+depression, of the cross-girders at the centre relative to their ends,
+when subject to the running load only, and supported at the middle and
+ends, the centre reaction being obtained as before indicated (1). This
+movement will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the upward
+flexure of the girder due to the centre reaction, considered as separate
+effects. Stress values having been estimated for the two conditions,
+these results may readily be deduced by simple flexure formulæ,
+observing that while the curve of moments due to live load sufficiently
+approximates to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter “Deflections,”
+the flexure due to the centre reaction will be but 0·80 of that which
+corresponds to the same stress for distributed loading. Or, the curve
+assumed by the girder under live load may be plotted by a method to be
+later explained.
+
+The sum of the movements now determined--that is, the live-load
+deflection of the outer girders, and depression, as is commonly the
+case, of the cross-girders--will give the extreme depression (marked _m_
+in Fig. 70), from the dead-load condition of the middle cross-girders,
+when supported to the extent desired by a centre girder whose
+proportions are not yet known, but which, carrying the required
+percentage of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the flanges of the
+new girder, governed by this flexure, will for a plate girder be
+
+  D × C × _m_
+  ----------- = _f_, unit stress on gross section (3)
+     S^{2}
+
+D and S being, as before (see “Deflections”), the depth and span
+respectively in feet, C a constant, _m_ the deflection in inches, and
+_f_ the stress per square inch on the gross section of flange.
+
+The gross area A, of the flange, is given by
+
+  S × _c_ × L{_t_}
+  ---------------- = gross area of flange (4)
+    8 × D × _f_
+
+_c_ × L{_t_}, being, as in (2), the load transferred to and carried by
+the centre girder.
+
+The actual stress in the flanges will, of course, be greater by an
+amount due to the girder’s own weight; but this does not affect the
+question of relief. For any ordinary case the stress per square inch
+will be low; but it will manifestly be useless to assume a greater
+stress with a view to economy, as the effect of reducing the section
+will simply be to make the girder too flexible, thus causing it to be
+less effective than primarily intended. If, as is seldom the case, there
+is freedom as to the depth of girder permissible, it is evident the unit
+stress may be made a condition, and the depth deduced by a suitable
+modification of formula (3); the relief desired being in this way
+equally well assured. Indeed, in the rare instances in which any depth
+may be adopted, this method is--contrary to the general rule--distinctly
+economical, particularly if the girder may be placed below the
+cross-girders, which simply rest upon it, without elaborate attachments.
+
+[Illustration: FIG. 71.]
+
+Considering now the second method of applying centre girders by which
+the new girder is made initially to carry part of the dead load, by
+adjustment, it will at once be recognised as a more complex matter. The
+measure of relief by which the old girderwork shall benefit need not be
+affected by the method of applying the centre girder, and may be decided
+on the principles already considered. The outer girders carrying a
+reduced load, when the bridge is fully loaded, and the cross-girders
+being in part supported at their centres in the manner already
+described, will give a resulting depression _m_ (see Fig. 71) of the
+centre cross-girders, below the original dead-load position, of a
+similar amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre girder, which may
+be designed to carry the required percentage of the total bridge loads
+with the maximum stress and depth, as conditions, leaving the initial
+dead load and necessary adjustments to be ascertained. This is the
+common case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.
+
+The centre girder of fixed depth being then required to carry a definite
+load at a definite flange stress, will deflect a definite amount at this
+stress. If this deflection equalled the extreme depression _m_ of the
+old girder work, no adjustment would be necessary, the centre girder
+then carrying no initial dead load, as by the first method; but for
+centre girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally being small,
+and in order to ensure that the new girder shall do its full work, some
+dead load must be put upon it. In the act of adjustment the
+cross-girders must be lifted and the centre girder depressed, till the
+joint movement equals the excess _s_ of the centre girder deflection
+over _m_, when the new girder will carry the proper amount of initial
+load, and upon further deflection under live load give the full measure
+of relief. The amount of “lift” or upward flexure of the old girder
+work, and the depression or “drop” of the new girder, during adjustment,
+will depend upon relative stiffness, and may be ascertained as
+follows:--
+
+For unit reactions at the centre of the cross-girders the upward flexure
+of these may be ascertained, as also the upward flexure of the two outer
+girders when subject to forces of the same total amount (one-half to
+each) applied at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are subject to
+unit lifting forces; similarly, the depression of the centre girder for
+unit loads applied at the cross-girders may be determined. There will
+then be known the movements upwards and downwards of the old and new
+work when being drawn together by unit forces applied as stated.
+
+If
+
+  _l_    = lift due to unit loads,
+  _l{t}_ = total lift due to adjustment,
+  _d_    = drop due to unit loads,
+  _d{t}_ = total drop due to adjustment,
+  _s_    = deflection excess = gross adjustment,
+
+there will then be
+
+     _d_
+  --------- × _s_ = _d{t}_,
+  _l_ + _d_
+
+total drop of centre girder under adjustment,
+
+     _l_
+  --------- × _s_ = _l{t}_,
+  _l_ + _d_
+
+total lift of centre cross girders under adjustment,
+
+  _d{t}_
+  ------ × unit load =
+   _d_
+
+initial load put upon centre girder at each cross-girder.
+
+The rise of the two outer girders for upward forces together equal to
+those depressing the centre girder may readily be deduced.
+
+[Illustration: FIG. 72.]
+
+[Illustration: FIG. 73.]
+
+The act of adjustment may conveniently be effected by the arrangement
+shown in Fig. 72, in which each cross-girder is hung up at its centre by
+four bolts. At the middle of the centre girder the total amount to be
+screwed up will be that corresponding to the deflection excess _s_, but
+towards the ends this amount decreases, and may advantageously be
+represented by a diagram as Fig. 73, in which, if _s_ represents to
+scale the amount to be screwed up at a centre cross-girder, the
+corresponding amounts for other girders may be read off direct. It will
+be apparent that it must be necessary to place the centre girder at
+such a height as to leave a space between the old and the new work
+greater than the amount to be screwed up, this excess clearance being
+ultimately filled by a packing.
+
+The precautions to be observed in carrying out this kind of work, and
+the practical methods of adjustment adopted by the author after some
+little experience, may here be given.
+
+Great care is necessary at the outset to ascertain the true spacing of
+the cross-girders, to ensure that the bolt-holes in the bottom flange of
+the centre girder shall come where desired. The fixing of the
+cross-girder brackets also needs close attention to avoid after trouble,
+the bolt-holes in the brackets being preferably drilled on the site
+after fixing. It will, for masonry abutments, be necessary to fix
+bedstones to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps leave the
+stones liable to settle slightly when the full load is carried. To
+eliminate the bad effect of this upon the ultimate adjustment, and to
+take up any initial set of the new girder work, which would be
+prejudicial in the same way, it is desirable, the centre girder being in
+place, to screw up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it is
+convenient to prepare, for use at the bridge, a diagram somewhat similar
+to Fig. 73, giving the amount by which the new and old work are to be
+brought together at each cross-girder, with the number of turns for each
+nut to effect this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is repeated as
+often as necessary, and so managed as to bring all up proportionately to
+the final requirement, keeping tally with chalk marks over each
+cross-girder as a check. The preliminary screwing up should be conducted
+with little less care than that adopted for the later adjustment, to
+avoid damage to the old work. This later adjustment having in due course
+been effected, it is then necessary to measure for packings to fill the
+spaces remaining between the old cross-girders and the new centre
+girder. These spaces should be callipered at each of the four corners,
+care being taken to avoid after-confusion. The measurements ascertained
+will, however, be too great for the finished packings, as an allowance
+of not less than 1/10 inch (total), will commonly be wanted to cover
+irregularities in the surfaces. The packings, having been prepared and
+checked, may be slipped into place after slacking all the bolts a small
+amount to permit this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last operation.
+
+As a check upon the calculations and adjustment, the “lift” of the outer
+girders and cross-girders, and the “drop” of the centre girder may be
+observed by levelling. For this purpose the author has used a staff of
+inches divided into tenths, with which, and a good level, very accurate
+readings may be taken for short distances.
+
+No reference has been made to the effect of skew in a bridge on the
+above methods, the explanation given applying rather to bridges square
+on plan. The influence of skew on the load distribution will largely be
+a matter of detailed calculation. The flexure of the girders may also be
+sensibly affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to modify the
+amount of screwing up during adjustment, which may be better understood
+by reference to Fig. 74, and comparing it with Fig. 73, the adjustment
+diagram for a square bridge.
+
+To illustrate how these methods of strengthening work out, and compare
+as to weights of centre girders required, the case has been assumed of a
+wrought iron bridge of 60-feet span, having outer girders 5 feet deep,
+of 39 square inches gross flange area; and cross-girders, at 8-feet
+centres, 27-feet span, 1 foot 9 inches deep, with a gross flange area of
+twenty square inches. The dead load and live load on either road are
+each 1·75 tons per foot run.
+
+The stress in the outer girders previous to the alteration being 6 tons
+per square inch gross, it is desired to relieve this to the extent of 33
+per cent. by a steel centre girder. In the table here given the
+quantities given in italics are fixed as primary conditions:--
+
+CENTRE STRENGTHENING GIRDERS FOR 60-FT. SPAN.
+
+  ----------------------------+-----------+------------+------------
+                              |  Centre   |  Centre    |
+                              |  Girder,  |  Girder,   |Adjustments
+             ----             |  Stress   |   Depth    | Unknown.
+                              |  Unknown. |  Unknown.  |
+  ----------------------------+-----------+------------+------------
+       _Outer Girder._        |           |            |
+                              |           |            |
+  Deflection under modified   |           |            |
+  live load                   |  ·42 in.  |  ·42 in.   | ·42  in.
+  Lift of adjustment          |   _nil_   |   _nil_    | ·153  „
+                              |           |            |
+      _Cross Girders._        |           |            |
+                              |           |            |
+  Depression under live load  |           |            |
+  --modified conditions of    |           |            |
+  support                     |  ·13 in.  |  ·13 in.   | ·13   „
+  Extreme depression (_m_)    |  ·55  „   |  ·55  „    | ·55   „
+  Lift of adjustment (cross-  |           |            |
+  girder only)                |   _nil_   |   _nil_    | ·095  „
+  Total lift of adjustment    |           |            |
+  (_l{t}_)                    |   _nil_   |   _nil_    | ·248  „
+                              |           |            |
+      _Centre Girder._        |           |            |
+                              |           |            |
+  Depth                       | _3·5 ft._ |  8·2 ft.   |_3·5 ft._
+  Unit stress on gross section|           |            |
+  (ex girder’s weight)        | 2·14 tons | _5·0 tons_ |_5·0 tons_
+  Total deflection (ex        |           |            |
+  girder’s weight)            |  ·55 in.  |  ·55 in.   |1·28 in.
+  Deflection excess (_s_)     |   _nil_   |   _nil_    | ·73  „
+  Depression, or “drop” of    |           |            |
+  adjustment (_d{t}_)         |   _nil_   |   _nil_    | ·482 „
+  Gross area of flange        |105 sq. in.|19·2 sq. in.|44·5 sq. in.
+  Weight                      |  20 tons  |  10·4 tons |11·4 tons
+  Net flange stress (including|           |            |
+  girder’s weight)            | 3·19 tons |  6·87 tons | 6·94 tons
+  ----------------------------+-----------+------------+------------
+
+Girders subject to distributed load are treated as having uniform
+stress, but where this is not strictly the case, as in some light
+girders, it will be necessary to take the fact into account. For centre
+girders of wrought iron, and a unit stress on the gross section of 4
+instead of 5 tons, the girder weights are between 9 and 10 per cent.
+greater.
+
+[Illustration: FIG. 74.]
+
+In the above treatment of the application of centre strengthening
+girders there is a source of error which should be touched upon. If,
+under live load, the centre girder deflects more than the outer girders,
+as it commonly will, there must be a want of uniformity in the behaviour
+of the cross-girders, those near the abutments being more relieved than
+the estimated amount of relief of those at the centre, which will have
+less than that intended; but the reduction of stress in the
+cross-girders will generally be so considerable that any such ambiguity
+of excess or defect is commonly unimportant; the effect of this also
+upon the main girders is much less than might be supposed, being, for
+the third of the cases just given, about 2-1/2 per cent. excess for the
+centre girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as approximate only.
+It is possible to eliminate some part of the error by lifting the end
+cross-girders during adjustment, a less amount than that given by the
+diagrams, Figs. 73 and 74, taking care that the centre girder is
+depressed its full amount by lifting the centre cross-girders a little
+more; this refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.
+
+Particulars are here given of five ordinary cases, comparing the
+calculated and observed results of adjustment. The operation of
+levelling was conducted by a quick-eyed and capable assistant, who was
+not made acquainted with the results expected, in order to avoid any
+sub-conscious tendency to match the calculated figures:--
+
+EXAMPLES OF CENTRE GIRDER ADJUSTMENTS.
+
+  ---------------------------------------+-----------+-----------------
+                    --                   |Calculated.|    Observed.
+  ---------------------------------------+-----------+-----------------
+                                         |   in.     |    in.
+                                         |           |
+                          No. 1.--56-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·82     |    ·84
+  Lift of cross-girders at centre        |   ·23     |    ·22
+  Lift of outer girders                  |   ·20     |·10 and ·13
+                                         |           |
+                          No. 2.--57-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·50     |    ·50
+  Lift of cross-girders at centre        |   ·18     |    ·20
+  Lift of outer girders                  |   ·11     |·08 and ·10
+                                         |           |
+                          No. 3.--67-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·70     |    ·75
+  Lift of cross-girders at centre        |   ·15     |    ·17
+  Lift of outer girders                  |   ·10     |    ·09
+                                         |           |
+                          No. 4.--68-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   ·70     |    ·65
+  Lift of cross-girders at centre        |   ·20     |    ·18
+  Lift of outer girders                  |   ·13     |    ·14
+                                         |           |
+            No. 5.--52-_Ft. and_ 28-_Ft. Spans continuous._
+                                         |           |
+                                         |Long |Short|Long |Short
+                                         |Span.|Span.|Span.|Span.
+  ---------------------------------------+-----+-----+-----+-----------
+                                         | in. | in. | in. | in.
+  Depression of centre girder            | ·28 | ..  | ·29 | ..
+  Lift of centre girder                  | ..  | ·04 | ..  | ·03
+  Lift of cross-girders (centre of spans)| ·17 | ·09 | ·15 | ·13
+  Lift of outer girders                  | ·08 | ..  | ·08 | ..
+  Depression of outer girder             | ..  | ·01 | ..  |negligible.
+  ---------------------------------------+-----+-----+-----+-----------
+
+The method of calculation adopted for these cases was not precisely that
+given, though depending upon the same broad principles. The first cannot
+be considered a good example. The last, having continuous girders, of
+course needed special treatment.
+
+Of about seventeen bridges strengthened in the manner described, the
+effect generally was satisfactory, in reducing deflection and vibration;
+but in two cases of small span, owing probably to settlement of
+bedstones, the results were not so good.
+
+From first to last the work of putting in a centre girder takes some
+little time, owing to the slow progress generally made in fixing the
+brackets, preparing packings, etc. The cost of a typical case was about
+23 per cent. of the cost of a new superstructure, with a 30 per cent.
+relief of stress.
+
+[Illustration: FIG. 75.]
+
+[Illustration: FIG. 76.]
+
+A special case of strengthening by a centre girder, having considerable
+interest, may be here referred to. The primary idea involved was not the
+author’s. The bridge dealt with has already been noticed under “Bracing”
+and a section, before alteration, shown in Fig. 26. The span being 85
+feet, there was no room for a centre girder of sufficient depth above
+the cross-girders and between the roads, nor was it considered
+economical to place the girder wholly below the floor, because of the
+costly staging this would have necessitated for erection purposes, the
+height above ground level being very great. A girder was therefore
+designed, having open latticing at an angle of 60 degrees, with a bottom
+boom to be below the cross-girders, the top being as high above the
+rails as could be permitted (see Figs. 75 and 76). A temporary boom was
+arranged at the intersection of diagonals, the lower boom proper not
+being fixed till the girder having been lifted into place, with the
+diagonal members passing between the cross-girders, allowed this to be
+done. The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being then 2 inches.
+The permanent boom was then put in place, and the girder restored as
+nearly as was practicable to the camber it was intended to have when
+complete, but without throwing, during the process, any improper loads
+upon the old work.
+
+The lower boom being finally riveted up, the cross-girders were made to
+bear upon it by suitable packings. There were, in addition to the new
+girder, two stiff frames between the old main girders, to which the new
+was secured.
+
+The girder was designed with the intention that under dead load only the
+cross-girders should just rest, but throw no weight, upon the new work,
+the latter assisting to carry live load only. The floor beams being of
+small span, and securely riveted to the old girder tops, the centre
+girder was required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion, the three
+points of support of the cross-girders thus not altering their relative
+levels. That this resulted was evident from the fact that, previous to
+connecting the cross-frames to the centre-girder, the work being
+otherwise complete, a space between the two of about 1/2 inch,
+afterwards filled by a packing, showed no alteration, the closest
+measurement failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be expected, very
+marked.
+
+In the conduct of that class of strengthening work which has been dealt
+with in this chapter, it is essential, in the author’s judgment, that
+the man responsible for the detailed calculations and design should
+himself see the operations of adjustment carried out, or delegate it
+only to one equally familiar with the requirements.
+
+Before dismissing the subject, it will be well to refer to a method of
+approximately determining flexure curves, of occasional use in dealing
+with centre girder or similar questions. The figure assumed is plotted
+to an exaggerated scale, with which object the actual radius of
+curvature at points along the girder’s length are first ascertained by
+the formula
+
+   E × D
+  ------- = R, radius of curvature in feet,
+  _f_ × 2
+
+and the radius of curvature for the diagram by
+
+  12 × R × F^2 = _r_, radius for plotting, in inches (5)
+
+E being the modulus of elasticity, D the girder’s depth in feet, _f_ the
+mean of the extreme flange stresses per square inch of gross area, and F
+the fraction indicating scale as 1/48, where 1/4 inch = 1 foot. The
+curve, being plotted, shows by direct scaling the movement of any point
+relative to its original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn with the help
+of template curves, or even set out as pieces of “straight.”
+
+When the curve is laid down so that its chord equals the span to scale,
+the method involves an error of excess in the resulting deflection or
+droop which is as much as 7 per cent. when the mean radius for plotting
+equals the span as drawn, or when the droop of curve approaches
+one-eighth of the span. As the exaggeration of curvature is made less
+pronounced, this error rapidly diminishes, till for a droop of about
+one-sixteenth the percentage is one-fourth part of that above given.
+This excess in the droop of curve may be amended by the following
+expression:--
+
+          (droop^3       )
+  droop - (------- × 3·73) = corrected droop, or deflection.
+          (chord^2       )
+
+For some purposes it may be preferable to amend the radii for plotting,
+so that the curve, as laid down, shall be correct, which may be
+effected by the formula here given, to be applied to each value of r, as
+first ascertained:--
+
+        (chord^2        )
+  _r_ + (------- × ·0625) = corrected plotting radius.
+        (  _r_          )
+
+If, however, the length of curve is made equal to the span (the chord
+then being less), and the radii for plotting as given by (5) are used,
+the result will for most purposes be sufficiently precise, though there
+will now be an error of a contrary kind, which, for a curve having a
+droop of one-eighth, will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described by
+Professor Fleeming Jenkin in the article “Bridges” of the “Encyclopædia
+Britannica,” but without corrections.
+
+A careful comparison of results by the above means, with those
+calculated, shows that with good draughtsmanship they may be relied upon
+for considerable accuracy. Equally applicable to girders of varying
+depth and flange stress, they have also a limited use in cases of
+continuity.
+
+[Illustration: FIGS. 77 and 78.]
+
+Figs. 77 and 78 illustrate the deflection and stress diagrams for the
+cross-girders of the bridge supposed to have been strengthened by a
+centre-girder, when under the influence of live load and a centre
+reaction of a definite amount. As a matter of convenience, each radius
+length has been halved, before correction, so that the resulting droop
+of the curve is twice the true amount.
+
+
+
+
+CHAPTER XII.
+
+CAST-IRON BRIDGES.
+
+
+Cast Iron as a material for bridges has of late years fallen into
+disrepute. It is now entirely tabooed by the Board of Trade for railway
+under-bridges, unless of arched construction. This condemnation of cast
+iron followed, and was apparently the result of, an accident which
+occurred to an under-bridge on one of the southern lines, which bridge
+had already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good, inasmuch as it
+led to a thorough overhaul of all railway under-bridges in this country,
+and the renewal of a great number no longer in a condition suited to the
+carriage of heavy or of passenger traffic; yet there is little doubt
+that, in the author’s judgment, many excellent cast-iron bridges were
+then removed at considerable cost, to be replaced by others of wrought
+iron or steel, which will not last so long as many of those displaced
+had done, or would still have lasted had they not been dismantled.
+
+The earlier cast-iron bridges were commonly made of cold-blast iron, a
+material of such strength and toughness as to give an extraordinary
+amount of trouble in breaking up the heavier parts, when the time
+arrived to do this, and with which material ordinary hot-blast iron is
+not to be compared for reliability.
+
+[Illustration: FIG. 79.]
+
+As illustrating the very considerable stress to which cast iron may be
+subjected, without of necessity leading to any mishap, two cases may be
+cited. The first, a bridge of 32 feet effective span, carrying two
+lines of way, each pair of rails being supported upon Barlow rails,
+forming the bridge floor, the ends resting upon the bottom flanges of
+inverted [T]-shaped girders, 2 feet 3 inches deep, as shown in Fig. 79.
+
+The extreme fibre stress works out at 2·9 tons per square inch in
+tension, and 5·9 tons per square inch compression, calculated as it
+would be in ordinary office work; but for the actual loads, at a span as
+above, exceeding the clear span by 6 inches only, and without regard to
+the effects of eccentric application of the load. The girders when taken
+out showed upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be too
+strongly condemned, notwithstanding that in this case no ill resulted.
+It is evident that a piece of the lower flange being broken out from
+this cause, as occasionally happens, might so reduce the section as to
+result in complete failure.
+
+[Illustration: FIGS. 80 and 81.]
+
+The second example is that of a small railway under-bridge of two spans,
+continuous over the central pier, each span being 16 feet 6 inches. The
+rails were supported upon longitudinal timbers lying within
+trough-shaped girders, as shown in Figs 80 and 81.
+
+The stress over the pier, in the extreme fibres of the top flange, is
+estimated at 4·7 tons per square inch in tension, but it should be noted
+that the effect of the timber longitudinal and rail has been neglected
+in arriving at this result, which might possibly on this account be
+reduced to near 3 tons per square inch.
+
+The case is noticeable because no evidence of high stress was apparent.
+The author saw nothing to suggest sinking of the central pier, the
+effect of which, within limits, would be to further reduce the stress as
+calculated; but it is quite possible some slight settlement had
+occurred; this, as the spans were so small, would have a sensible
+effect. While too much reliance should not, it is clear, be placed upon
+any estimated result about which there is a lingering doubt, it should
+be remarked that, as it would be necessary the pier should sink 3/16 of
+an inch, for each ton of reduced stress, it is not probable that the
+results quoted are in excess to any material degree; they are, indeed,
+more probably low, as no notice has been taken of impact.
+
+Though cast-iron girders for railway under-bridges are now prohibited in
+this country for new works, there are still uses to which they may be
+applied, and it may be well to insist that girders of this material
+should be fairly loaded, the weight being brought upon them in such a
+way that there shall be no serious secondary stress, such as arises when
+wide flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking down under a
+load fairly applied. Preference is now given to steel or wrought iron
+for columns; while this is often quite justifiable, there remain many
+cases in which nothing better need be desired for this purpose than good
+cast iron, provided only that the column be loaded in a suitable
+manner--i.e., axially, and that the arrangement and details of the
+super-structure are such that there shall be no cross-breaking efforts,
+or rocking of the column due to temperature or other causes; unless,
+indeed, such cross-breaking or rocking is definitely taken into account
+in designing the work. The same care observed in the detailing of
+cast-iron work that is not infrequently taken in the design of
+structures made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with the
+advantage of greater resistance to rust, and a reduced cost in
+maintenance.
+
+Good cast iron is, in fact, when used with discretion, a most excellent
+material, popular predjudice notwithstanding. The oldest metallic bridge
+in this country at the present moment is of that metal.
+
+The one chief respect in which cast iron is at a disadvantage compared
+with wrought iron or steel is that it does not give premonitory warning
+of failure--it remains intact, or it breaks. The indications of
+weakness, which may be read by an experienced inspector of other
+metallic bridges, are in a great measure absent. There is also an
+objection which may exist, but is to be avoided by good design and care
+in the foundry--viz., internal stress due to unequal cooling. In extreme
+cases this may lead to fracture before the work has left the maker’s
+hands, but it can only occur by neglect of ordinary precautions.
+
+[Illustration: FIGS. 82 and 83.]
+
+In a case which has already been referred to in the chapter on
+“Deformations,” page 80, an outer rib of a cast-iron arch fractured near
+the crown after fifty-four years’ use. Owing to the nature of the
+design, and the fact that the near abutment had closed in slightly,
+bringing the linear arch of necessity near the lower edges of the arch
+segment in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces, at the
+upper edge where fracture commenced. The result was very far from
+explaining the occurrence of the break, but an examination of the
+details shown in Figs. 82 and 83 will make it apparent that, in addition
+to the tensile stress, as calculated, there was probably a severe
+initial stress of the same character due to irregular cooling in the
+foundry half a century before. The sum of these stresses, it is
+suggested, placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent either by
+producing a small further settlement of the foundations, of which the
+author saw no evidence, or, as is more probable, the attachment of a
+rope to this rib for the purpose of keeping a barge in position, which
+certainly did occur, gave the arch rib just such an additional strain as
+to result in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The inner ribs
+were of a much less objectionable section.
+
+[Illustration: FIG. 84.]
+
+Cast-iron arches, though still allowed by the Board of Trade rules, are,
+indeed, liable to be seriously affected by settlement, or yielding of
+the abutments, unless hinges at the crown are introduced. As an instance
+of this may be quoted a bridge of some 45 feet span, in which the arches
+were cast in two pieces abutting, and very efficiently bolted together
+at the crown, the springing and vertical abutment member of the
+spandrel being bolted and built solidly into heavy masonry. The arch
+sank at the crown, caused by, or itself the cause of, a movement of the
+abutment, with the result that the lower bolts at the crown joint broke
+away, rupturing the casting, as shown in Fig. 84. The arch must then
+have acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if a proper
+hinge had originally been provided. The break happened to occur so as to
+leave a sufficiently good bearing face at the crown; there was, indeed,
+no tendency for one surface to slide upon another; but in the accidental
+fracture of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.
+
+A second case of very much the same character has also been under the
+author’s observation, though in this the ends of the spandrels were not
+built into the brickwork of which the abutments were composed. Other
+instances of fracture either in the arch proper or in the spandrel work,
+have come under notice, though particulars cannot now be adduced; but
+the examples cited are by themselves sufficient to justify the
+conclusion that it is imprudent to construct a cast-iron arch without a
+central pin or its equivalent, unless the abutments, being exceptionally
+well founded, may be relied upon as free from any liability to move. It
+is, however, to be borne in mind that movement in the abutments of a
+small arch of any given absolute amount is more injurious than the same
+amount of movement in the abutments of large arches of similar design,
+so that what may be negligible in the latter case would perhaps be
+destructive in the former.
+
+To the absence of ductility and liability to initial stress must be
+added yet another disadvantage to which cast-iron work is prone--viz.,
+the possibility of concealed defects, blow-holes or cold-shuts; these in
+good foundry practice are not very likely to occur, but, as they are
+possible, cannot be overlooked in considering the suitability of cast
+iron for bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks by way of
+qualification, the author reiterates his opinion that there is still a
+use for cast iron in bridgework.
+
+With respect to the repair of cast-iron bridges, but little is to be
+said; the possibilities in this direction are very limited. Occasionally
+it may be desired to deal with the fracture of some member in the
+spandrel bracing of an arch, when it is commonly sufficient, and even
+preferable, to limit the repair work to confining the fractured parts in
+such a way as to prevent displacement.
+
+Rarely it may happen that an arch fractures as a result of settlement,
+or other movement, when, if it is decided that safety of the structure
+is not imperilled, it will in this case also be preferable to confine
+the parts simply by flitch-plates or other contrivance, with no attempt
+rigidly to make good the break, the consequences of which treatment
+would probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable, though
+something may occasionally be done by the negative process of lightening
+the dead load, or by remodelling the permanent way. Arches may, however,
+be rendered much more reliable by the introduction of suitable bracing
+where this is either wanting or inefficient.
+
+In scheming such additions it is desirable to arrange for as little
+drilling of the old work as is possible; where this cannot be altogether
+avoided, the position of the holes should be carefully chosen with
+regard to the effect they may have upon the strength of the old work.
+
+
+
+
+CHAPTER XIII.
+
+TIMBER BRIDGES.
+
+
+Timber bridges, though probably the most ancient in type, are yet the
+least durable in any particular instance. The perishable nature of the
+material when used for exposed construction renders it peculiarly liable
+to develop defects which quickly put a limit to the life of the
+structure. In addition to decay in the body of the main members--which
+may perhaps be long delayed, so that a simple beam bridge may last for
+many years--there is in more complex designs decay at connections and
+joints, which proves very detrimental to the integrity of the whole.
+Water running upon the surface of a member gravitates to its lower end,
+and, if there be a joint or other connection, settles there, to be
+productive of lasting mischief. From this cause, together with a very
+common deficiency of bearing surface relative to the forces to be met,
+the joints soon develop some movement; working of the structure
+commences under passing loads, its final destruction being then a
+question of time only. Each joint is, in fact, in timber bridge
+construction a source of serious weakness to a degree which has no
+parallel in well-designed metallic bridges.
+
+Wrought-iron straps to confine the ends of raking members, or for other
+uses, are liable to crush into the wood, and bolts are apt to enlarge
+the hole through which they pass. Wood keys, where these are introduced
+to prevent one timber from sliding upon another, are also prone to
+develop cracks in the main members, and fibre crippling from excess of
+stress. All these defects are, however, in timber-work more easily
+defined than efficiently remedied, as it is barely practicable for any
+but the harder woods to ensure, for heavy loads, a sufficiency of
+bearing surfaces.
+
+The most readily detected evidence of deterioration in timber bridges is
+the sag of its bearing members, or trusses, for the simple reason that
+if there is no local trouble at the joints, there will probably be no
+appreciable drop at the centre of the span. The existence of such a
+depression may, however, be caused in rare instances by the spread of
+the supporting piers or abutments, particularly in the case of beams
+trussed by end diagonal rakers and having no tie.
+
+Bridges formed of deep trusses, with the road upon the top, are
+sometimes found to be wanting in lateral bracing, the result of which is
+that the main trusses go out of line, leaning considerably one way or
+the other, being checked only by such rigidity as the joints and
+floor-beam attachments may have, with possibly some assistance from the
+end connections of the span.
+
+The decay of piles where entering the ground or water is, of course, a
+fruitful source of trouble, as also is the sinking of piles, where these
+are insufficient in number, or have not been well driven in the first
+place.
+
+A vital difficulty with timber structures generally is the uncertainty
+that will commonly exist as to how far decay extends in those cases
+where it has started. Timber does not necessarily show upon its surface
+the evidences of internal rotting. Memel timber may, indeed, be
+sometimes found to have become thoroughly unreliable, yet showing no
+sign of this upon its painted surface. By sounding the wood with a
+hammer, or by probing, its condition may commonly be ascertained. In
+cases of doubt, an auger-hole will make it clear as to whether the
+interior be good or otherwise, as to the particular parts tested; but
+only as to those parts, leaving it a matter of guesswork as to the
+remainder.
+
+[Illustration: FIG. 85.]
+
+A railway bridge having many of the defects which have been indicated
+may be quoted as an example. This structure crossed a canal, supported
+upon piles, some of which were in water, others carrying land spans. The
+canal span consisted of four trusses, one under each rail, or nearly so,
+framed in the manner shown in Fig. 85, precise details not, however,
+being now available. The trusses, apart from deflection under live load,
+sagged considerably--in one instance, 4-1/2 inches; one inside truss was
+also leaning towards the centre line of the bridge as much as 3 inches.
+One raker, or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections and joints
+were also in a bad condition. The vertical tie-bolts of the main trusses
+were all slack. The piles generally, many of which were badly decayed,
+had sunk and inclined towards one end of the bridge about 4 inches in 7
+feet of height, the ground being soft and unreliable.
+
+Movement under a passenger train crawling over the bridge was very
+appreciable, but not startling. There had been introduced, from time to
+time, additional timbers and iron ties, with the object of rendering the
+spans more reliable, but leaving it somewhat difficult to determine the
+function of the several members. The bridge was, of course,
+reconstructed.
+
+[Illustration: FIG. 86.]
+
+[Illustration: FIG. 87.]
+
+[Illustration: FIG. 88.]
+
+An instance may here be cited showing how badly distorted a timber
+structure may become without actually falling. The bridge referred to
+consisted of three spans of 29 feet, each span having two trusses,
+between which ran a colliery tramroad, 1-foot 6-inch gauge; the corves
+running upon this, at 4 feet 6 inch centres, weighed, when full, about
+10 cwt. each. The trusses were badly out of shape, the centre span
+having sagged 5-1/2 inches, with one truss of the same span nearly 10
+inches out of line at the centre. This little bridge, of which some
+details are shown in Figs. 86, 87, and 88, had been in use about twenty
+years.
+
+[Illustration: FIG. 89.]
+
+A third case which may be named is that of a road bridge, about 12 feet
+wide, crossing by thirteen spans a shallow river liable to floods. The
+construction was of a simple character, as indicated in Fig. 89, and
+consisted of piles supporting trussed beams, which had sagged in some
+instances over 2-1/2 inches. The bridge had, some years previous to the
+author’s inspection, been heavily repaired, many new strut and
+stretching pieces having been introduced, the piles also being
+reinforced or renewed. Five years before, a traction engine, said to
+weigh 5 tons, had passed across the bridge in safety; but the author
+noticed that a coal wagon, which, with the horse, weighed about 50 cwt.,
+when walked slowly over set up much movement. This bridge had been in
+use nearly thirty years, and was very much out of line from end to end.
+
+Though timber bridges cannot at the best be considered durable, yet, by
+attention to certain points in design and construction, their length of
+life may be materially enhanced. Every cut across the grain may be
+considered an element of weakness by exposing the material to quicker
+decay, for which reason the number of ends, or of joints, should be
+reduced to a minimum. An additional reason for reducing the number of
+joints or other connections is the liability of these to develop
+movement, as already stated, the yield of any one joint, being the cause
+of movement in others, which might, but for this, have remained close.
+These considerations lead to the conclusion that fewness of parts is, in
+timber construction, as in structural work generally, an excellent
+principle to observe. Mortising, elaborate scarf joints, recessing, or
+any cutting into the timber which is not essential, should be avoided,
+the simplest forms of connection being preferable, if at all suitable.
+If a step or butt surface is wanted for any member, it is commonly
+better to provide this by a cleat or other added piece, rather than by
+cutting into the timber butted against.
+
+A complicated joint formed in the body of main timbers can only be
+renewed by renewal of the timber itself, whereas by the method indicated
+the joint is readily tightened, or re-made, without involving the main
+member. Bearing surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake of bearing
+surface in the holes, and reduction of any liability to bend under
+cross-stress. In trusses of the form shown in Figs. 85 and 86, it is
+desirable to introduce diagonal members in the middle bay, even though
+it may appear that the stiffness of the main beams is sufficient to
+render this unnecessary as a matter of strength, as without these there
+is apt to be, under rolling load, a slight distortion, leading to
+working of the joints and free entry of moisture. Lateral bracings
+should also, for much the same reasons, be introduced, even though they
+may not appear necessary in the new structure, with joints all close and
+effective.
+
+Projecting ends of timbers should be carried out well beyond the
+requirement of strength or bearing, in order to ensure a liberal margin
+for that decay in the end fibres which commonly develops. Timbers
+resting upon abutments, or running into confined spaces, should be
+arranged for free ventilation and ready drying. Occasionally joints at
+the lower ends of timbers are protected by lead or zinc flashings to
+prevent water running into them, a method which should have some
+protective value. Whatever measures may be adopted, whether in the
+design or execution of timber bridge-work, will, however, be but little
+effective, if the timber itself is not good of its kind, and well
+seasoned.
+
+Creosoting to be useful should be thorough and something more than skin
+deep. The timber itself should be well dried before treatment.
+
+The repair of timber bridges very largely consists in the renewal of
+decaying timbers, where this is practicable, or in adding supplementary
+pieces where the old cannot conveniently be displaced. Joints may be
+tightened up by hard-wood wedges, properly secured to prevent slacking
+back, all bolts being also screwed up tight, perhaps some additional
+being introduced.
+
+Piles standing in water, which have decayed, may be strengthened by
+driving other piles between the old, or on either side, but not of
+necessity opposite to them, and by means of waling timbers bolted to the
+old piles, put in a position to take load, either by the walings resting
+upon their tops, or being bolted to them. Piles decayed where entering
+solid ground may generally be strengthened by bolting on supplementary
+timbers to reach well above and below the decayed part, or by cutting
+out the bad length, introducing a new piece, and fishing the butt-joints
+in a proper manner. But all remedial measures have generally to be
+considered with reference to cost, as compared with the probable
+increase of life of the structure. With a bridge in an advanced state of
+decrepitude, such repairs may prove anything but economical, and at the
+best defer reconstruction but a very moderate length of time.
+
+
+
+
+CHAPTER XIV.
+
+MASONRY BRIDGES.
+
+
+Masonry bridges, in which description it is intended to include
+structures both in stone and brick, are, when well built, amongst the
+most durable and long-suffering of any which come under the care of a
+maintenance engineer; yet when developing the faults peculiar to their
+kind, they may be the occasion of much anxiety, and render necessary
+frequent inspection, or even continuous watching.
+
+Apart from decay of mortar or material, defects may very commonly be
+traced to the foundations, or to earth-slips. Sinking, when uniform, may
+be quite harmless, though possibly inconvenient; irregular sinking of
+piers or abutments is quite a different matter. It is, however,
+remarkable to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and kind which would
+be fatal to the connections of metallic bridgework is endured by bridges
+of stone or brick; not, it may be, without damage, yet with no occasion
+for alarm. The superstructure of metallic bridges may often, however, be
+restored to the true level before the mischief has become serious,
+whereas in the case of masonry arches this is not practicable.
+
+Spreading of the abutments is very seldom the cause of any great injury
+to an arch, though it is common enough to find old and flat arches
+slightly down at the crown; but the contrary case of abutments closing
+in is not very unusual when these are high, or terminate a viaduct over
+a deep valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected; or, if the
+arches are very solid and heavy, the abutment may slide forward at the
+base, with no sensible reduction of the opening.
+
+When a viaduct connects the two ends of a high embankment, it may happen
+that the end piers are not clear of the embankment slope, in which event
+a pier may, should the bank slip, move with it, as to that part not in
+solid ground; with the result, in a bad case, that it is broken across
+and the superstructure imperilled.
+
+[Illustration: FIG. 90.]
+
+A case of abutment movement is illustrated in Fig. 90, which represents
+the end arch of a masonry viaduct, one abutment of which had moved
+forward in the manner already referred to. From the springing upwards
+the arch retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the movement became
+pronounced, heavy timber centering was introduced, with the object of
+preventing any mishap, the damaged portions being ultimately cut out and
+made good. The structure was thirty-five years old.
+
+The practical utility of stop piers in long arched viaducts is, perhaps,
+rather in checking movement of the tops of piers under moving load than
+in arresting actual failure of a series of arches. That the tops of
+piers do move very sensibly need not be doubted. The author has
+attempted to measure this in the case of piers about 60 feet to the
+springing, by means of a theodolite placed below, but has reached no
+more definite result than that a movement existed, of which he was not
+able to determine the amount. If in a viaduct some arches are more
+heavily loaded than others, each spreading slightly, the end piers of
+the group will move amounts which together equal the sum of the
+individual span spreads, with a tendency in the arches beyond those of
+the group overloaded to rise.
+
+This rocking may be detrimental both to the piers and arches, and helps
+to account for the disintegration of mortar in arches and piers, which
+not infrequently happens. The soffits will sometimes be seen with a
+thick incrustation of lime, which has washed out of the joints, or from
+limestone ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that pieces of stone
+or brick will drop out, necessitating repair at heavy expense, of which
+scaffolding is commonly a large part.
+
+Tall piers may be found badly out of the upright due to sinking of
+foundations. A marked case of this kind came under the author’s
+notice--a viaduct of fifteen semicircular arches, in which, though many
+piers were wanting in truth, one in particular was about 1 foot 4 inches
+out of vertical, making one side of the shaft plumb, and doubling the
+normal batter of the other. Inquiry showed that in this instance the
+pier had never been upright from its earliest history dating back
+thirty-six years. This makes clear the desirability, to avoid hasty
+conclusions, of ascertaining, when it is possible to do so, the complete
+record of any structure.
+
+A bridge fifty-eight years old, of three skew spans, carrying a railway
+over a canal, and having somewhat flat brick arches with stone quoins
+upon low piers, developed the somewhat unusual defect, as to the centre
+arch, of splitting along its length for about 10 feet, parallel to and
+some 7 feet from one face. In this case there was reason to believe that
+there had been considerable local settlement of the piers on that side
+of the bridge. The arches were otherwise in bad condition, the brickwork
+poor, and the mortar decayed. Each arch was down at the centre, and
+displayed a fault not unusual where bad brickwork joins up to good cut
+stonework, the quoins showing a tendency to separate from the brick
+rings. Below the bridge were coal-workings.
+
+Brick arches built in parallel rings sometimes separate one ring from
+the other, demonstrating the known propriety of bonding the rings
+together properly, and of carrying the arch round, when building, at its
+full thickness.
+
+[Illustration: FIG. 91.]
+
+An instance of bridge failure from a somewhat peculiar cause may be
+quoted as of some interest, largely because the structure was very
+ancient, having been in existence some 400 years. This bridge, carrying
+a road, was of the type usual in old masonry bridges over a river,
+having small arches, thick piers, and solid backings to the arches. Two
+flood-openings at one end had, by sinking and want of care, become
+partly closed. The centre arch had, however, been widened about 140
+years previously. During a severe flood, the swollen river, overflowing
+its banks, trespassed upon a timber yard a little above bridge, and
+washed down into the stream a large quantity of sawn timber; this,
+unable to get through the main arch with freedom, compacted into a
+serious obstruction. The flood water, thus checked in its passage, seems
+to have scoured below the timber, and robbed the piers of such support
+as they formerly had (see Fig. 91). The bridge stood in this condition
+till the water lowered, when the middle part of the structure broke up,
+and subsided into the hole which had been washed out. But for the
+monolithic character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers stood had
+been partly undermined for very many years. The case is instructive, as
+showing how a slight accident--powerless by itself to work mischief--may
+be very damaging when allied with so powerful an agent as running water.
+
+[Illustration: FIG. 92.]
+
+The enduring character of even the roughest class of masonry arch, if
+only the material be good and abutments stable, is shown when it becomes
+necessary to destroy old work of this character. Fig. 92 represents a
+short length of “cut and cover” arching in process of demolition, just
+before it fell in. The masonry was of hard sandstone rubble and had been
+cut away, as shown, till at the point A only a very small piece of the
+arch remained, when the length finally broke up and dropped. Arches have
+commonly a great reserve of strength; tunnel linings are, indeed, often
+badly out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed or bulged,
+to serve the purpose intended.
+
+Though the equilibrium of masonry arches has been the occasion of much
+profound study, and the nicest calculation has sometimes been applied to
+the design of such work, yet it appears that when an arch is well backed
+up, the theoretical linear arch need have but little connection with the
+figure of the intrados; a statement consonant both with common-sense and
+the teachings of experience. With solid backing, this would indeed seem
+to be more important than any part of the arch ring below the top of the
+backing, the lower part of the ring serving chiefly to preserve the face
+of the solid work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure would seem to
+be inevitable. The masonry or brickwork does not always show evidence of
+damage, if the distortion has been slow; suggesting that structures of
+this kind have a power of accommodation with which they are not
+generally credited.
+
+A noticeable cause of deterioration of masonry structures, which may be
+quite independent of settlement, is serious vibration. This is well
+known in connection with church belfries, and is also locally apparent
+when telegraph or other poles are attached to masonry parapets.
+Vibration, when caused by heavy railway traffic, acting upon arches
+light or originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially built, and
+particularly those carrying ordinary roads, and not subject to much
+vibration, have great lasting powers, if repaired with skill, or even
+let alone. Distortion of the arch may be quite consistent with practical
+stability, if the movement or decay with which it originated is not
+progressive, or has been arrested. In this connection a distinction is
+to be made between arches well backed, to which the foregoing remarks
+apply, and in which the two halves of each arch may act as separate
+monoliths meeting at the crown, and the case of a true arch ring
+independent of any outside resistance, such as backing or spandrels may
+give, and depending almost wholly upon the proper balance of its
+component voussoirs for its stability. With the latter class of
+structure no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way, and the work
+is dealt with judiciously, if at all. It must, however, be understood
+that there are limits as to what may be done effectively, short of
+rebuilding, in dealing with structures in which, perhaps, brickwork is
+rotten and mortar decayed and crumbling, the whole being little better
+than a broken mass of rubbish.
+
+In cases where it may be prudent to introduce safety centring, as in an
+instance already referred to, it is commonly expedient to refrain from
+causing this to take any sensible part of the load till all movement has
+ceased, the centres being at the outset largely precautionary. The
+requirement with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement is still going
+on, the effect may be to cause the arch to break up upon the centring,
+and precipitate repair work which might otherwise have been left to a
+more convenient time, when all movement had stopped or been checked by
+suitable measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt with
+piecemeal by cutting out the bad places, a small part at a time, and
+making good. The work requires the greatest care of experienced men.
+
+Pointing masonry or brickwork is effective for little other than
+protective purposes, and to check further weathering; it has obviously
+no effect upon the interior work, and if made to cover up the evidences
+of internal decay, is even misleading and objectionable. In extreme
+cases it may be desirable to open out the road and deal with the
+filling, to relieve or to strengthen the outer spandrel walls, which
+sometimes bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise repairing solid backing,
+in which operations some regard must be had to the effect of the work
+upon the balance of the opposing halves of the arch.
+
+Of the different classes of masonry commonly used in bridgework, it may
+be well to remark that good coursed rubble, or preferably that variety
+bonding both vertically and horizontally, of a durable stone, perhaps
+quite unfit for any but rough dressing, may make a most lasting
+structure, the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from the block,
+probably along some line of relative weakness--there is no “nursing” of
+weak corners; whereas with stones reduced to a perfectly regular shape
+by chisel work, the plane surfaces and geometrical angles are made with
+partial regard only to the natural grain of the stone.
+
+
+
+
+CHAPTER XV.
+
+LIFE OF BRIDGES--RELATIVE MERITS.
+
+
+The life of bridges of differing materials has been incidentally touched
+upon by the examples quoted, in dealing with each class of structure. It
+will be useful to recapitulate some of the facts adduced, and to compare
+the terms of life so far as they appear to be indicated; but in doing
+this it is necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history. The
+duration of any such structure may be limited by adverse conditions,
+peculiar to the case considered, by defects of design, material, or
+workmanship--present from the first--or by neglect, overloading, or
+accident, making up its later record.
+
+With the exception of timber structures, it is difficult to find any
+class of bridges furnishing examples which have reached the limit of
+life, independently of the evils named, and as a result of unavoidable
+decrepitude. There are none the less influences at work tending to this
+condition, and which it is too much to expect can in all cases be
+foreseen or completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and minor
+faults in design, which even in the most capable hands may be expected
+ever to fall short of perfection. At the best, then, the life of any
+structure, though long, must have a limit. With bridges of more average
+or inferior qualities the life may be positively short, even without the
+destructive influence of overloading.
+
+Dealing with instances of metallic bridges, the adjacent table gives the
+time each had been in existence when removed, and some indication of the
+reason for its condemnation. Those marked with an asterisk were cases of
+pronounced high stress. From a study of the table it appears that in
+actual practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and thirty-six
+years; but these figures applied to this collection of cases only. It is
+to be remarked that many other bridges outlasted these, and are likely
+to continue reliable. These results show, then, no more than that some
+wrought-iron bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as indicating that
+the durability of such structures is by no means so limited as the table
+would suggest. It is to be observed that, as design and maintenance are
+now better and more generally understood than when experience was
+largely wanting, it is to be expected that later examples will show no
+such poor results.
+
+Of steel bridges little can be said, because of the limited time this
+material has been in use; but the generally acknowledged belief, quite
+in agreement with the author’s observation, that steel rusts more freely
+than wrought iron, suggests that such bridges will have a shorter lease
+of life, the more so that the surface-to-section ratio is also greater
+for higher unit stresses, though other adverse influences are much the
+same for one material as for the other.
+
+Of cast-iron structures but few cases have been given; of these,
+cast-iron arches have been noticed as developing defects which led to
+reconstruction, or to limiting the loads to be carried. Plain cast-iron
+girders, on the other hand, have never, under the author’s direct
+observation, been removed for any other reason than because they were
+cast iron, or from over-stress, due to the growth of loads; never from
+defects or wasting, though it is not suggested no such cases exist. The
+author has no evidence which points to what may be the limit of life of
+a good cast-iron girder fairly treated.
+
+_Examples of Life of Metallic Bridges._
+
+  -------------------------+-------+------+----------------+------------
+        Description.       | Span. | Age. |   Defect.      | Reference.
+  -------------------------+-------+------+----------------+------------
+                           |ft. in.|Years.|                |
+                           |       |      |                |
+                                _Wrought Iron._
+                           |       |      |                |
+  Plate girders            |  (?)  |  12  |Loose rivets    |
+    *Ditto                 | 35  0 |  12  |Ditto           |p. 52
+     Ditto                 | 55  0 |  14  |Rust. Distortion|pp. 78 & 97
+  Trough girders           | 11  0 |  16  |Loose rivets.   |p. 50
+                           |       |      |Cracked webs    |
+  Plate girders            |  (?)  |  22  |Loose rivets    |
+  Twin girders             | 31  6 |  23  |Weak. Cracked   |p. 13
+                           |       |      |webs            |
+     Ditto                 | 35  6 |  23  |Weak. Distorted.|p. 74
+  Plate girders            | 42  0 |  23  |Loose rivets.   |p. 21
+                           |       |      |Cracked webs    |
+     Ditto                 | 72  0 |  29  |Weak. Loose     |p. 53
+                           |       |      |rivets          |
+     Ditto                 | 47  0 |  24  |Distortion      |p. 9
+     Ditto                 | 32  0 |  32  |Rust. Cracked   |p. 14
+                           |       |      |webs            |
+    *Ditto                 | 25  0 |  36  |Weak            |p. 63
+                           |       |      |                |
+                                  _Steel._
+                           |       |      |                |
+  *Trough girders          | 15  8 |  32  |Weak. Rusted    |pp. 68 & 98
+                           |       |      |                |
+                                _Cast Iron._
+                           |       |      |                |
+  *Girders                 | 32  0 |  36  |Weak            |p. 141
+   Girders, cast-iron piles|  (?)  |  44  |Ditto           |
+   Arches                  | 45  0 |  55  |Crack. Settle-  |p. 145
+                           |       |      |ment            |
+     Ditto                 |100  0 |  62  |Crack. Deforma- |pp. 80 & 145
+                           |       |      |tion            |
+  -------------------------+-------+------+----------------+------------
+
+With timber bridges the length of life appears to be about twenty-five
+years, but this is very largely dependent upon the question of
+maintenance, and may range from fifteen to thirty-five years. It is
+manifest that repairs, when extensive and consisting of the renewal of
+the more essential parts of the structure, border upon reconstruction,
+and may be continued indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for railway
+bridges, be taken as stated, though for highway bridges possibly longer.
+
+Of masonry bridges little is to be said but that it is only in cases of
+bad work or material--with, perhaps, vibration or settlement--that these
+have a shortness of life comparable with that of defective metallic
+bridges. Where these adverse conditions obtain, heavy repairs may be
+necessary before the structure is many years old; but, under reasonably
+fair conditions, bridges of masonry may be expected to outlast
+structures in any other material. Apart from road-bridges which are
+admittedly long-lived, there are a large number of railway bridges and
+viaducts of masonry which, despite heavy loads and vibration, have been
+in use for the past seventy years.
+
+Dealing with the cost of maintenance, this with bridges of wrought iron
+or steel should result simply from scraping and painting, with such
+other incidental work as may be necessary on the subsidiary materials
+used in the structure. The cost of painting will vary with the height
+and character of the bridge, and the amount of scaffolding, if any, and
+may be from 5_d_. to 1_s_. or more per square yard; this if distributed
+over five years, a not unusual interval between each painting, works out
+at an appreciable figure, which may vary from one-third to one per cent.
+of the first cost, per annum. The yearly cost of painting steel-work
+will, for shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be necessary,
+repairs and possibly strengthening, which may raise the total cost of
+maintenance very considerably.
+
+Cast-iron bridges, being less liable to rust, cost less for painting
+than other metallic bridges; and if the cast iron is closed in by
+masonry, practically nothing; they do, indeed, involve very little
+expenditure in the maintenance. Not being very amenable to repair or
+strengthening, cast-iron bridges commonly remain very much as built, or
+are reconstructed.
+
+The proper care of timber bridges may become costly as the structure
+gains in age, and soon grow to a very wasteful expenditure. This is
+evident when it is considered that repairs may be necessary after ten
+years, and that whatever may have been the cost of any part when new, it
+cannot be replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions to be
+observed in dealing with an old structure carrying its load. In addition
+to ordinary repairs, there will be paint or other protective coating to
+be applied, though this is not always done.
+
+The upkeep charges of masonry bridges will be practically nothing in
+favourable cases; but, on the other hand, where extensive repairs become
+necessary, may reach a considerable amount. Exceptional outlays are,
+however, infrequent, and may be spread over a large number of years, in
+those rare instances in which they become imperative.
+
+  _Durability._      _Maintenance     _First Cost._
+                     Charges._
+
+  Masonry            Masonry          Timber
+  Cast Iron          Cast iron        Masonry
+  Wrought iron       Wrought iron     Steel
+  Steel              Steel            Cast iron
+  Timber             Timber           Wrought iron
+
+For purposes of ready comparison, placing bridges of the materials under
+review in order of durability, they would appear as in column 1 of the
+table above; in order of low maintenance charges, generally as in column
+2; and in order of low first cost, as in column 3. With respect to the
+question of first cost, the arrangement of the third column applies only
+to small bridges, say, up to 70-foot span; and, being liable to
+variation with the conditions, is but approximately correct. The less
+costly descriptions of masonry are alone considered in this connection.
+
+It may be added that the total yearly charge of interest on first cost,
+redemption, and maintenance, appears to be for masonry bridges, about
+one-half only of the corresponding totals for bridges of wrought iron,
+steel, or timber; those of cast iron taking an intermediate place.
+
+Summarising the above considerations, and dealing with the relative
+merits of bridges in the different materials, it may be broadly stated
+that for conditions at all suitable nothing seems to be superior to
+masonry--including in this description first-class brickwork--whether
+for road or railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little affected by
+increase of loads. The mass of a masonry arched structure is so great,
+and the margin of strength commonly so liberal, that considerable
+increments of load may have but little effect upon the reliability of
+the structure.
+
+Cast iron has, for bridges of simple design, a strong claim to the
+second place, though its want of ductility is a demerit. It can,
+however, have but a limited use in bridge construction, being applicable
+only to small girder spans and skilfully-designed arched structures.
+
+For bridges of moderate span in which the question of cost does not
+control the matter, wrought iron should probably come next, steel being
+best reserved for those of a larger size, in which weight of the
+structure greatly affects economy.
+
+Timber may be regarded as a material rarely to be used in this country
+for structures to occupy a permanent place, unless for urgent economic
+reasons of the moment.
+
+While expressing this general view of the matter, it is to be admitted
+that the propriety of these conclusions is somewhat discounted by the
+difficulty there now is in obtaining cast iron of the desired
+toughness, or wrought iron with promptitude and sufficient variety of
+section at a reasonable price.
+
+It is apparent, also, that the choice of material may be largely
+influenced--even determined--by considerations of headway, construction
+depth, or character of foundations; so that no very definite rules can
+be usefully laid down, though the adoption of unsuitable materials has
+not been so unusual as to make these suggestions altogether
+purposeless.
+
+
+
+
+CHAPTER XVI.
+
+RECONSTRUCTION AND WIDENING--CONCLUSION.
+
+
+The need for the reconstruction of bridges, arising from various causes
+which have been treated in the preceding chapters, original weakness or
+faults in design, decay or defects, may also be caused by such
+extraneous considerations as the growth of loads, widening of the
+openings spanned, or improvement of the headway.
+
+In any case, a precise survey or measuring up of the structure and its
+immediate surroundings is required, in the execution of which the
+greatest care is desirable, and with respect to which it may be well to
+give a few hints.
+
+The surveying chain, when used, should be tested, the measure of
+accuracy required rendering this imperative in a degree peculiar to work
+of this class. Linen tapes should also be compared with a reliable steel
+tape, and used only where sufficiently accurate for the particular
+purpose. A careful and observant man may do very good work with a linen
+tape, making just that allowance in the sag of the tape which corrects
+for the inevitable stretch; but there is still some uncertainty involved
+in its use, and the author prefers to rely upon a steel tape,
+notwithstanding the inconvenience commonly experienced from its
+intractable nature and liability to damage.
+
+Instruments used must also be in the best adjustment; as errors, which
+in ordinary field work may not be of great importance, are inadmissible
+in bridge work.
+
+It is not necessary here to enter upon the methods of small survey
+work, but it may be desirable to point out that abutment walls should be
+plumbed for verticality; girders, which are liable to be leaning,
+defined in position by reference to their bearings; and generally that
+it should never be taken for granted that there is truth in old work, or
+that this may be assumed as to line or level.
+
+In cases where disputes with any local authority as to headway are
+likely to arise, it is prudent to supplement the information as to level
+of soffits by rods cut to length in strict agreement with the clear
+height, before removing the old superstructure.
+
+It is apparent that in cases where the superstructure is already
+condemned, the detail measurements may be confined to that part of the
+structure which is to remain, securing only such information as to the
+work superseded which may be required in arranging for the new work.
+
+In taking particulars of skew bridges, needless as the warning may seem,
+it is yet necessary to remark that there may be right or left-hand skews
+which will not reverse. The author has known a disregard of this to make
+serious trouble in two instances.
+
+Dealing first with reconstruction of the superstructure of railway
+under-bridges, these, if small, may not give much trouble, though the
+demand for greater strength will, perhaps, involve some difficulty in
+working to the limiting construction depth--i.e., the distance from the
+top of rail to soffit of bridge--particularly as many old bridges have a
+very niggardly allowance in this respect. It may be, and quite commonly
+is, necessary to raise the rails a small amount, or, if headway is not
+restricted, to lower the soffit. Clearances between the running gauge
+and girder-work may also be difficult to secure, more liberal allowances
+being now required than formerly. Complications in the character of the
+permanent way, so frequently found upon old bridges, should, of course,
+be got rid of, if possible; but the endeavour may introduce further
+difficulties. Regard must throughout be had to the methods to be adopted
+in removing old work and in erecting the new. Perhaps the simplest case
+to deal with is that where girders lie parallel to, and under the rails,
+with a timber floor upon which the permanent way is carried, as sections
+of the road involving pairs of girders may be readily removed, and
+replaced by the new girder-work (see Fig. 93). If the deck be of trough
+flooring or old rails, the matter may not be so simple, as regard must
+then be had to the position of joints in the existing floor, and the new
+work be schemed with respect to the number and office of girders which
+may be got in at any one breaking of the road. A slight slewing of rails
+may sometimes be resorted to on occasion, where this has the effect of
+releasing some part of the work not otherwise to be dealt with.
+
+[Illustration: FIGS. 93 and 94.]
+
+Bridges having main girders, with timber or trough flooring resting upon
+the bottom flanges, or suspended by bolts, will, if carrying many roads,
+cause some little difficulty, as the dismantling of any one span
+involves the disturbance of others; where, however, many lines are
+concerned, it may be feasible to put one or more temporarily out of use,
+preserving the continuity of traffic over those which remain, but
+refraining from any diversion of the more important roads.
+
+Somewhat similar troubles occur where main girders with cross-girders at
+the lower flanges are found, particularly if the cross-girders are
+arranged in line, the ends abutting on each side of the same main girder
+webs. It is seldom, however, that this construction is used in bridges
+of small span carrying many roads; but where it does occur, it may
+necessitate the use of timbering below, to carry the ends of
+cross-girders when freed from their supporting main girders. (See Fig.
+94.)
+
+[Illustration: FIG. 95.]
+
+If it is proposed to use new main and cross-girders, it is desirable to
+arrange these in the manner already recommended, the cross-girders not
+in line; this has peculiar advantages in reconstruction work, as the
+bolting up and riveting of the cross-girder ends is not hampered by
+other cross-girder attachments, leaving each piece of floor complete in
+itself. Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence of
+one span from those adjoining (see Fig. 95); but the method is wasteful
+of space, and involves a somewhat greater total weight in the main
+girders.
+
+The foregoing observations apply more generally to small single-span
+bridges, the operations on which may be effected without any material
+disturbance of traffic arrangements; though this can seldom be wholly
+avoided, it should be confined, where practicable, to a few hours on a
+Sunday.
+
+The reconstruction of bridges over 70-feet span may have to be dealt
+with under more elaborate arrangements, if carrying two lines only,
+possibly with single-line working for a period more or less protracted;
+or it may be necessary, having regard to the weight of main girders to
+be removed, to carry the whole structure upon temporary staging,
+supporting the road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed erection in
+its ultimate position, or by erection at one side and drawing across.
+The latter method is, however, commonly reserved for cases in which no
+special staging is used under the old structure.
+
+Bridges of a number of openings are usually dealt with by securing full
+possession of one road at a time, which for double-line bridges
+necessitates single-line working. It is commonly out of the question,
+even with moderate spans, to deal with some of these only at a time, and
+so avoid continuous possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new main
+girders do not in any way interfere with those of the old, and where it
+is not necessary to reset bed-stones, or make other alterations in the
+bearings which necessitate the complete clearance of the pier-tops. In
+exceptional cases it may be found possible to arrange for the complete
+removal of a small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.
+
+Spans erected to one side of the final position, to be later travelled
+across, are commonly mounted upon gantry staging, and up to 50 tons
+weight may rest directly upon rails well greased. The power adopted to
+move the span is usually that of screw or hydraulic jacks, or
+occasionally engine haulage, special tackle being in that case necessary
+to apply the engine power in the right direction. If the time is
+limited, or weight considerable, a more elaborate arrangement by which
+the load is supported upon wheels, may be necessary, with a view to
+reducing the resistance to a manageable amount. All work which it is
+possible to do before shifting into place, including the permanent way,
+where this is of a special character, should be executed in advance,
+leaving only the rail connections to be made good when the span is in
+position.
+
+Where timber staging is used to carry the permanent way before
+dismantling an old structure, it is convenient to begin by placing stout
+balks of timber under the sleepers from end to end of the bridge, or
+directly under the rails if space is limited; the staging is then
+arranged to give support to the running timbers.
+
+Metallic under-bridges of ample headway, perhaps over coal-workings
+(since settled down), or for some less sufficient reason made of metal,
+may be cheaply replaced by brick arches built below the old
+superstructure, the springings of the arch being checked into the face
+of the existing abutments. With stout walls, careful work and good
+material will make this an efficient and durable job.
+
+It being a primary condition of reconstruction work to interfere but
+little with ordinary traffic arrangements, single-line working is
+avoided wherever practicable; as this, always objectionable, may
+necessitate the erection of special signals and signal apparatus,
+besides the temporary remodelling of the roads, and in this country may
+involve also a Board of Trade inspection--altogether a troublesome and
+expensive business.
+
+Any bridgework which is accompanied by breaking or blocking the road can
+only be undertaken by arrangement with the traffic department, after
+notice duly given and published in the periodical record of such
+matters; it is generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand as is
+possible. Wherever practicable and prudent, the whole work is released
+from its surroundings, masonry cut away, rivets cut out and replaced by
+good bolts, nuts removed from holding down bolts, or the bolts cut
+through, etc. Particular care should be exercised to ascertain what
+remains to be done immediately prior to removal. It is necessary further
+to arrange for trucks to be in readiness to receive old material, and
+others containing new girder work to be conveniently stationed, having
+been loaded up to come right end foremost; engine power, cranes, empty
+and loaded trucks, being all marshalled and so placed as to be available
+in proper order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or as to the
+reach of the crane in effecting its work.
+
+The whole operation to be conducted on any Sunday should be well within
+the resources of the men and plant engaged in it, or so managed that it
+is a matter of no serious importance if the whole cannot be completed as
+originally desired.
+
+Possession of the roads to be blocked having been secured between
+certain hours, if some part only of the work to be carried out has been
+completed as the time grows short, any attempt to execute the remainder
+may result in checking trains until such time as the line may be
+reported clear--a contingency to be avoided--though the temptation to
+save another Sunday’s work by delay of a few minutes to some one train
+may be considerable.
+
+In scheming any reconstruction, it may be insisted that at least one
+feasible method of carrying out the work must be secured, though it is
+the author’s experience that frequently some other method than that
+contemplated is in the end adopted, when, some months later, the final
+arrangements for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered, with a view
+to a moderate amount of work being done at any one time, and to achieve
+as much more as he can himself secure by scheming, or a liberal use of
+labour; all Sunday work, with attendance of engines and cranes, being of
+necessity expensive.
+
+Railway over-bridges do not commonly present any particular
+difficulties. The spans to be dealt with are usually small, and the
+weights to be lifted moderate. The height above rails may, however, be
+above the lift of any crane; and, for the purpose of raising main
+girders, a derrick may become necessary, the rearing and guying of which
+may block many roads during the time it is in use. The girders of larger
+spans, too unmanageable to be lifted whole, may be erected upon staging;
+to secure the requisite headway it may be necessary to build the girders
+at a level above that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the staging.
+
+The widening of railway under-bridges is, as a rule, a matter of no
+special difficulty, but some remarks may be of use. Widenings should be
+planned with a regard to later reconstruction of the original bridge, if
+that is at all likely to be necessary, and with the object that, when
+complete, the whole should be a consistent piece of work.
+
+It may, indeed, happen that widening of a bridge may involve the
+remodelling or reconstruction of the old work, to enable the new roads
+to be laid down as desired; this is more likely to be necessary where
+there exist main girders not competent to take any additional load, and
+to duplicate which would sacrifice space between the new and old roads;
+or it may be unavoidable because of slewing of the old rails, as part of
+a general rearrangement.
+
+[Illustration: FIG. 96.]
+
+Dealing with widenings simply, there is often some little trouble in
+contriving a connection between the new and the old work, as this may
+have to be made under, or close to, the sleeper ends of the existing
+roads. It is desirable to arrange this part so that no drilling of old
+work for rivets or bolts shall be necessary, there being, in fact, no
+strict connection. By judicious scheming, this may be effected, whilst
+securing freedom from leakage of water at the joint. (See Figs. 96 and
+97.) If tying of the new and old structure is desired, this can usually
+be done quite simply, well below the floor at some more accessible
+level.
+
+[Illustration: FIGS. 97 and 98.]
+
+The strict jointing-up of trough flooring, new to old, at right angles
+to the troughs, cannot be contemplated, but may be dealt with by
+treating each part independently, the ends being near together,
+separated by the space of an inch or so. Each trough end being closed up
+by a diaphragm or oak block to prevent ballast dropping through, the top
+of the space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions to
+take away leakage, as it is practically impossible to make this
+arrangement “drop dry” under the conditions common in executing work of
+this kind (see Fig. 98).
+
+[Illustration: FIGS. 99 and 100.]
+
+Where trough flooring, new and old, has to be made good parallel to the
+troughs, the difficulty of making a direct connection is less marked,
+and it is not unusual to introduce a strip cover simply; but if
+accessible, the work is still troublesome, as there is commonly a want
+of strict alignment and truth as to level, between the new and the old
+troughs. It is preferable to arrange for junctions of a more convenient
+type, as in Figs. 99 and 100.
+
+When widening masonry arch bridges by girder-work, it is desirable to
+insure that any girders parallel to the masonry face shall be
+sufficiently far removed from it to enable painting to be executed. The
+space remaining between the girder and the arch may then be bridged by
+floor-plates, or an extension of the timber floor if that is adopted.
+
+In effecting a junction such as this, the author has used the
+arrangement shown in Fig. 101, the advantage being that the piece of
+connecting-floor is sufficiently wide, and also sufficiently flexible,
+to allow the girder-work freedom to deflect without doing harm. The load
+carried by the width of floor is, as to one part, delivered well on to
+the old masonry, in preference to being imposed near to the face. If it
+should for any reason be imperative to place the girder close to the
+arch face, it is preferable to scheme the floor so that there shall be
+no actual contact, the new floor in that case slightly overhanging the
+masonry, as in Fig. 102, or dealt with as in Fig. 103, if depth is
+restricted.
+
+The widening of masonry arch bridges by masonry, calls for no other
+remark than that the new work should be free from the old; though it may
+be advisable, when the widening is narrow, to tie the new work to the
+old in such a way as to permit independent settlement.
+
+If the widening is exceptionally narrow, there may be no choice but to
+bond the new and old work together, and in the best manner, with the
+object of minimising the risk of separation.
+
+[Illustration: FIGS. 101 and 102.]
+
+[Illustration: FIG. 103.]
+
+The above matters relative to widenings, though apparently trifling, may
+by neglect cause much trouble and expense in maintenance. They
+principally concern small bridges, the extension of larger structures
+coming rather in the category of independent works.
+
+
+CONCLUSION.
+
+In bringing these chapters, dealing largely with questions affecting
+maintenance, to a close, it may be well to draw attention to the fact
+that economy in design (apart from improper reduction of sections) goes
+hand-in-hand with economy of upkeep. Given good material, that which
+favours low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to girders,
+favours also small expenditure in maintenance. The less complex the
+design, the easier will it be to keep the structure in order; the less
+the number of parts, the fewer will be the connections. Freedom from
+smithing eliminates liability to failure at cranks, or other work which
+has been subject to fire. It is apparent also that the free use of
+rolled instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A liberal depth
+to all girders, by reducing deflections, limits the inclination of the
+ends and gives the connections a better chance of remaining intact.
+Lastly, with work of this character, the labour of scraping and painting
+is simplified and cheapened.
+
+The author wishes to reiterate the statement made in the opening
+paragraphs of this book, that all instances of decrepitude, failure, or
+peculiar behaviour cited, have been under his direct observation. The
+fact is insisted upon simply that the reader may appreciate that the
+information is at first hand.
+
+It has not been thought necessary, nor was it considered desirable, to
+indicate the locality of each case referred to; but it may be said that
+the matter of these chapters has been accumulating during many years,
+and relates to structures under the control of many different bodies.
+
+The study of old bridges is strongly recommended, particularly with
+respect to stress and strain, which in structures new or old, occur
+possibly as may be expected--certainly as they must. Consideration of
+existing work may thus be a useful check upon the fanciful requirements
+of some methods of design. There is a recent tendency, for instance, in
+English practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many old bridges
+carrying their loads with no sign of distress, should have failed long
+ago. Excess in riveting is a common extravagance, to which the same
+criticism may in a less degree apply. Considerable impact allowances for
+girders of large span may also be referred to as an application of
+empiric theory not justified by experience, which, as in all cases where
+such considerations fight with facts, should be modified or rejected.
+
+
+
+
+INDEX
+
+
+  Abutments, leaning, 82, 173
+  -- movements of, 158
+  -- settlement of, 78
+  Adjustment of centre girders, 128
+  -- of distributing girders, 120
+  Angular distortions, 88
+  Arches, equilibrium of, 162
+  -- repair of, 163
+  Arrangement of cross girders, 21, 175
+  Asphalt, 26
+
+  Ballast, 29
+  Bearing pressure on rivets, 47, 51, 57
+  Bearings, skew, 4
+  Bottom booms, end bays, 18
+  Bracing, additional, 117
+  -- effects of, 34
+  -- flat bars, 37
+  -- incomplete, 41
+  -- sea piers, 42
+  Bridge floors, 20
+  -- repairs, 107
+  -- surveys, 107
+  Bridges, life of, 165
+  Breaks in [T] bars, 16
+  Buckling of webs, 16
+
+  Camber, 24, 80
+  Cast-iron arches, 80, 145
+  -- -- bridges, 141
+  -- -- columns, 7,144
+  -- -- girders, 141
+  -- -- in sea water, 101
+  Centre girders, 122
+  Cinder ballast, 29
+  Cold-blast iron, 141
+  Cooling stresses in cast iron, 145
+  Construction depth, 173
+  Corrugated sheeting, 29
+  Cost of centre girders, 135
+  -- of maintenance, 168
+  Counterbracing, 19
+  Cracked bedstones, 3
+  -- columns, 7
+  -- web plates, 13, 14, 15, 50
+  Cross girder arrangement, 21
+  -- girders, fixed ends, 22, 118
+  -- -- rusted, 29, 97
+  -- -- weak, 30, 66
+
+  Decay and painting, 96
+  -- of floor plates, 109
+  -- of timber, 28, 150
+  Deflection, 85
+  -- due to booms and web, 86
+  -- exceptional cases, 88
+  -- in new and old work, 85
+  -- working formulæ, 87
+  Deformations, 73
+  Depth of girders, 23, 89, 184
+  Diagonal ties, 19, 42
+  Distortion due to temperature changes, 79, 84
+  Distributing girders, 120
+  Drainage holes, 25
+  “Drop” loads, 89
+  Dwarf walls under floors, 26
+
+  Early steel girders, 68
+  Economy, 184
+  Effect of earth slips, 157
+  -- of floor on deflection, 88
+  -- -- -- on stresses, 23, 30
+  -- of high stress, 86
+  -- of permanent way on stresses, 18
+  --of skew on bridge floors, 25
+  -- -- -- on centre girders, 131
+  -- of transverse bracings, 34
+  -- of vibration on masonry, 162
+  -- of wave action on sea piers, 42
+  End bays, bottom booms, 18
+  Equilibrium of masonry arches, 162
+  Examination of bridges, 107
+  Examples of cast-iron bridges overstressed, 141
+  -- of high stress, 70
+  -- of life of bridges, 167
+  -- of rivet stress, 56
+  -- of strengthening, 114
+  -- -- -- by centre girders, 131, 134
+  Excessive bearing pressure, 51
+
+  Faulty workmanship, 80
+  Fixed ends to cross girders, 22, 118
+  Flange stresses, 63, 66, 67
+  Flanges, side loaded, 9, 73
+  Flat bar bracing, 37
+  Flexing of girders, 9, 74, 76
+  Flexure curves, 138
+  Fractured bedstones, 3
+  -- rails, 30
+  -- webs, 13, 14, 15, 50
+  Fractures in cast iron, 7, 145
+
+  Girder bearings, 2
+  Girders on columns, 7
+  -- on masonry, 8
+  Girderwork in masonry, 101
+
+  Headway, 173
+  High stress, 61
+  -- in cast iron, 141
+  -- in rivets, 47, 52
+  Holes for drainage, 25
+
+  Impact, 20, 62
+  Inclination of girder ends, 23, 53
+  Incomplete bracing, 41
+  Initial set, 88
+  Interference with traffic, 177
+
+  Jack arches, 29, 101
+  Joints in rails, 29, 109
+  -- in trough floors, 28, 180
+  Junction between metallic and masonry bridges, 183
+  -- -- new and old masonry bridges, 182
+  -- -- new and old metallic bridges, 180
+
+  Lattice girder stresses, 47-66
+  Liberal depth to girders, 23, 89, 184
+  Life of bridges, 165
+  Limit of elasticity, 61
+  Linen tapes, 172
+  Longitudinal floor girders, 23
+  Loose rivets, 21, 25, 51, 53, 56, 109
+
+  Main girders, 9-17
+  Masonry bridges, 157
+  -- enduring character of, 161
+  Memel timber, 150
+  Methods of calculation, 46, 61
+  -- of observing deflection, 90
+  -- of setting out deflection curves, 138
+  Movements of abutments, 158
+  -- of cast-iron bridge, 82
+  -- of piers, 42, 83, 159
+  -- of rollers, 7
+  -- of wrought-iron bridges, 4, 21, 38, 73
+
+  New members to old work, 116
+
+  Oiling steelwork, 99
+  Old drawings unreliable, 108
+  -- rivets, 21, 51, 54, 55
+  Open webs, 17
+  Overhead bracing, 39
+  -- girders, 118
+
+  Painting, 98
+  Parapets, 79
+  Permissible stress in old work, 110
+  Piers, movements of, 42, 83, 159
+  -- out of plumb, 159
+  Piles, decay of, 102, 150
+  Pitch pine, 28
+  Plasticity, 61
+  Plate webs, 9
+  Plated floors, 23, 25, 30
+  Pointing masonry, 164
+  Proposed rivet stresses, 58
+
+  Quickly applied loads, 89
+
+  Rail joints, 29, 109
+  Rails, breaks in, 30
+  Reaction of cross girder with centre support, 127
+  Red-lead, 98, 100
+  Relative merits of bridges, 169
+  Relief by centre girders, 122
+  Repainting, 100
+  Repair of bridges, 107, 147, 155, 163
+  -- of timber piles, 156
+  Replacing flange plates, 110
+  -- rivets, 111
+  Resistance of cast iron to rust, 101
+  Riveted connections, 45, 86
+  Rivets in cramped positions, 20
+  -- in cross girder ends, 21, 49, 53, 54
+  -- in road bridges, 60
+  -- in webs of main girders, 46
+  -- spacing of, 60, 80
+  -- stresses in, 56
+  Rocking of piers, 8, 83, 159
+  Roller bearings, 7
+  Rubble masonry, 161-164
+  Running load and deflection, 95
+  Rusting, instances of, 29, 96
+  -- of steelwork, 99
+  -- over sea-water, 98
+
+  Sag in timber bridges, 150
+  -- of tapes, 172
+  Scour under piers, 161
+  Sea piers, 42, 102
+  Setting bedstones, 3, 129, 176
+  Settlements, 76, 157
+  Skew bearings, 4
+  -- bridges, right and left, 173
+  -- -- floors, 25
+  Skirting plate, 26
+  Slope of girder ends, 92
+  Softening of cast-iron in sea-water, 101
+  Spacing of rivets, 60, 79
+  Spread of abutments, 157
+  Spring joints, 23
+  Steel trough girders, 68
+  -- troughing, 70
+  Stiffening girders from floor, 12, 40
+  -- to webs, 16, 38, 185
+  Stop piers, 158
+  Strength of light top booms, 40
+  Strengthening of bridges, 107, 122
+  -- bridge floors, 118
+  -- cross girders, 123
+  Stress in plated floors, 31
+  Study of old bridges, 185
+
+  Tall piers, 42, 159
+  Timber bridges, 149
+  -- floors, 27
+  -- staging, 177
+  Top booms, 18
+  Traffic during reconstruction, 177
+  Transverse bracing, 34, 117
+  Trough floors, 27, 180
+  -- girders, 50, 74
+  [T] stiffeners, breaks in, 16
+  Twin girders, 15, 75
+  Twisting of girders, 11, 68, 73
+  -- -- -- corrected, 12
+  Types of reconstruction, 174
+
+  [U]-shaped booms, 18
+  Uncomplicated stress, 62
+  Uniform pressure on bearings, 6
+
+  Value of E in deflection formulæ, 87
+  Vibration, 162
+
+  Wasted webs, 14, 29, 96
+  Water, scour of, 161
+  Web buckling, 16
+  -- plates, cracked, 13, 14, 15, 50
+  -- rivets, 46, 50
+  -- stiffening, 16, 38, 185
+  Widening masonry bridges, 182
+  -- metallic bridges, 179
+  Wide spaced rivets, 79
+  Wind pressure, 41, 43
+
+  Yielding of piers, 8, 83, 159
+
+
+  LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
+  GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
+
+
+
+
+Transcriber's Notes:
+
+The text of the original work (including inconsistent spelling,
+hyphenation, formatting etc.) has been retained, except as mentioned
+below.
+
+The slight differences between the Table of Contents and the text have
+not been changed.
+
+Changes made to the text:
+
+Some punctuation errors and obvious typographical errors have been
+corrected silently.
+
+Several illustrations have been moved to where they are described in the
+text.
+
+Page 123, formula (2): the original shows an unclear superscript after
+the first L. As described in the following line of the text, this has
+been changed to L{_l_}.
+
+
+
+
+
+End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
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+Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Anatomy of Bridgework
+
+Author: William Henry Thorpe
+
+Release Date: December 6, 2013 [EBook #44371]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ANATOMY OF BRIDGEWORK ***
+
+
+
+
+Produced by Chris Curnow, Harry Lam� and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+
+Transcriber's Notes:
+
+Text between underscores represents _italics_, small capitals have been
+transcribed as ALL CAPITALS.
+
+Curly brackets indicate {subscripts}; letters between square brackets
+(such as [T] and [U]) represent the shape rahter than the letter itself.
+
+More Transcriber's Notes may be found at the end of this text.
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+  BY
+
+  WILLIAM HENRY THORPE
+  ASSOC. M. INST. C. E.
+
+  WITH 103 ILLUSTRATIONS
+
+  [Illustration]
+
+  London
+  E. & F. N. SPON, LIMITED, 57 HAYMARKET
+  New York
+  SPON & CHAMBERLAIN, 123 LIBERTY STREET
+
+  1906
+
+
+
+
+PREFACE
+
+
+In offering this little book to the reader interested in Bridgework, the
+author desires to express his acknowledgments to the proprietors of
+"Engineering," in which journal the papers first appeared, for their
+courtesy in facilitating the production in book form.
+
+It may possibly happen that the scanning of these pages will induce
+others to observe and collect information extending our knowledge of
+this subject--information which, while familiar to maintenance engineers
+of experience, has not been so readily available as is desirable.
+
+No theory which fails to stand the test of practical working can
+maintain its claims to regard; the study of the behaviour of old work
+has, therefore, a high educational value, and tends to the occasional
+correction of views which might otherwise be complacently retained.
+
+  60 WINSHAM STREET,
+  CLAPHAM COMMON, LONDON, S.W.
+  _October_, 1906.
+
+
+
+
+CONTENTS
+
+
+  CHAPTER I.
+
+  INTRODUCTION--GIRDER BEARINGS.
+
+                                                                    PAGE
+
+  Pressure distribution--Square and skew bearings--Fixed bearings--
+  Knuckles--Rollers--Yield of supports                                 1
+
+
+  CHAPTER II.
+
+  MAIN GIRDERS.
+
+  _Plate webs_: Improper loading of flanges--Twisting of girders--
+  Remedial measures--Cracks in webs--Stiffening of webs--[T]
+  stiffeners                                                           9
+
+  _Open webs_: Common faults--Top booms--Buckling of bottom booms--
+  Counterbracing--Flat members                                        17
+
+
+  CHAPTER III.
+
+  BRIDGE FLOORS.
+
+  Liability to defects--Impact--Ends of cross and longitudinal
+  girders--Awkward riveting--Fixed ends to cross girders--Plated
+  floor--Liberal depths desirable--Type connections--Effect of "skew"
+  on floor--Water-tightness--Drainage--Timber floors--Jack arches--
+  Corrugated sheeting--Ballast--Rail joints--Effect of main girders
+  on floors                                                           20
+
+
+  CHAPTER IV.
+
+  BRACING.
+
+  Effect of bracing on girders--Influence of skew on bracing--Flat
+  bars--Overhead girders--Main girders stiffened from floor--
+  Stiffening of light girders--Incomplete bracing--Tall piers--Sea
+  piers                                                               34
+
+
+  CHAPTER V.
+
+  RIVETED CONNECTIONS.
+
+  Latitude in practice--Laboratory experiments--Care in considering
+  practical instances--Main girder web rivets--Lattice girders
+  investigated--Rivets in small girders--Faulty bridge floor--
+  Stresses in rivets--Cross girder connections--Tension in rivets--
+  Defective rivets--Loose rivets--Table of actual rivet stresses--
+  Bearing pressure--Permissible stresses--Proposed table--Immunity of
+  road bridges from loose rivets--Rivet spacing                       45
+
+
+  CHAPTER VI.
+
+  HIGH STRESS.
+
+  Elastic limit--Care in calculation--Impact--Examples of high stress
+  --Early examples of high stress in steel girders--Tabulated
+  examples--General remarks                                           61
+
+
+  CHAPTER VII.
+
+  DEFORMATIONS.
+
+  Various kinds--Flexing of girder flanges--Examples--Settlement
+  deformations--Creeping--Temperature changes--Local distortions--
+  Imperfect workmanship--Deformation of cast-iron arches              73
+
+
+  CHAPTER VIII.
+
+  DEFLECTIONS.
+
+  Differences as between new work and old--Influence of booms and web
+  structure on deflection--Yield of rivets and stiffness of
+  connections--Working formul�--Set--Effect of floor system--
+  Deflection diagrams--Loads quickly applied--"Drop" loads--Flexible
+  girders--Measuring deflections--New method of observing deflections
+  --Effect of running load                                            85
+
+
+  CHAPTER IX.
+
+  DECAY AND PAINTING.
+
+  Examples of rusting of wrought-iron girders--Girder over sea-water
+  --Rate of rusting--Steelwork--Precautions--Red-lead--Repainting--
+  Scraping--Girders built into masonry--Cast iron--Effect of sea-
+  water on cast iron--Examples--Tabulated observations--Percentage of
+  submersion--Quality of metal                                        96
+
+
+  CHAPTER X.
+
+  EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+  Purpose--Methods of examination--Calculations--Stress in old work--
+  Methods of reducing stress--Repair--Loose rivets--Replacing wasted
+  flange plates--Adding new to old sections--Principles governing
+  additions--Example--Strengthening lattice girder bracings--Bracing
+  between girders--Strengthening floors--Distributing girders        107
+
+
+  CHAPTER XI.
+
+  STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+  Principal methods in use--Method of calculation--Adjustments--
+  Connections--Method of execution--Checks--Effect of skew on method
+  considered--Results of calculation for a typical case--Probable
+  error--Practical examples--Special case--Method of determining
+  flexure curves                                                     122
+
+
+  CHAPTER XII.
+
+  CAST-IRON BRIDGES.
+
+  Limitations of cast iron--Stress examples--Advantages and
+  disadvantages--Foundry stresses--Examples--Want of ductility of
+  cast iron--Repairs--Restricted possibilities                       141
+
+
+  CHAPTER XIII.
+
+  TIMBER BRIDGES.
+
+  Perishable nature--Causes of decay--Sag--Lateral bracing--Piles--
+  Uncertainty respecting decay--Examples--Conditions and practice
+  favourable to durability--Bracing--Protection--Repair--Piles--Cost 149
+
+
+  CHAPTER XIV.
+
+  MASONRY BRIDGES.
+
+  Definition--Cause of defects or failure--Spreading of abutments--
+  Closing in--Example--Stop piers--Example of failure--Strength of
+  rubble arch--Equilibrium of arches--Effect of vibration on masonry
+  --Safety centring--Methods of repair--Pointing--Rough dressed
+  stonework                                                          157
+
+
+  CHAPTER XV.
+
+  LIFE OF BRIDGES--RELATIVE MERITS.
+
+  Previous history--Causes of limited life--Tabulated examples of
+  short-lived metallic bridges--Timber and masonry bridges--
+  Durability--Maintenance charges--First cost--Comparative merits--
+  Choice of material                                                 165
+
+
+  CHAPTER XVI.
+
+  RECONSTRUCTION AND WIDENING OF BRIDGES.
+
+  CONCLUSION.
+
+  Measuring up--Railway under-bridges--Methods of reconstruction in
+  common use--Reconstruction of bridges of many openings--Timber
+  staging--Traffic arrangements--Sunday work--Railway over-bridges--
+  Widenings--Junction of new and old work--Concluding remarks--Study
+  of old bridgework                                                  172
+
+  INDEX                                                              187
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK.
+
+
+
+
+CHAPTER I.
+
+INTRODUCTION.
+
+
+No book has, so far as the author is aware, been written upon that
+aspect of bridgework to be treated in the following pages. No excuse
+need, therefore, be given for adding to the already large amount of
+published matter dealing with bridges. Indeed, as it too often happens
+that the designing of such constructions, and their after-maintenance,
+are in this country entirely separated, it cannot but be useful to give
+such results of the behaviour of bridges, whether new or old, as have
+come under observation.
+
+In the early days of metallic bridges there was of necessity no
+experience available to guide the engineer in his endeavour to avoid
+objectionable features in design, and he was, as a result, compelled to
+rely upon his own foresight and judgment in any attempt to anticipate
+the effects of those influences to which his work might later be
+subject. How heavily handicapped he must have been under these
+conditions is evident from the mass of information since acquired by the
+experimental study of the behaviour of metals under stress, and the
+growth of the literature of bridgework during the last forty years. That
+many mistakes were made is little occasion for surprise; rather is it a
+cause for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the study of defects
+and failures, even though they be of such a character that no
+experienced designer would now furnish like examples.
+
+Modern instances may, none the less, be found, with faults repeated,
+which should long since have disappeared from all bridgework, and are
+only to be accounted for by the unnatural divorce of design and
+maintenance already referred to. As the reader proceeds, it may appear
+that details are occasionally touched upon of a character altogether too
+crude and objectionable to need comment; but the consideration of these
+cases is none the less interesting, and, so far as the author's
+observation goes, not altogether unnecessary.
+
+Most of the instances cited are of bridges, or parts of bridges, of
+quite small dimensions; but it is these which most commonly give
+trouble, both because the effects of impact are in such cases most
+severely felt, and possibly because the smaller class of bridges is very
+generally designed by men of less experience, than large and imposing
+structures.
+
+The particulars given relate in all cases to bridges of wrought iron,
+unless otherwise described.
+
+An endeavour has been made to secure some kind of order in dealing with
+the subject, but it has been found difficult to avoid a somewhat
+disjointed treatment, inseparable, perhaps, from the nature of the
+matter. Finally, the reader may be assured that every case quoted has
+come under the writer's personal notice.
+
+
+GIRDER BEARINGS.
+
+In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing allowed. Clearly,
+the surface over which the pressure is distributed should be
+sufficiently ample to avoid overloading and possible crushing or
+fracture of bedstones where these exist; but if no knuckles are
+introduced, this is an extremely difficult matter to insure. A long
+bearing may deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.
+
+If the girder is made with truly level bearings, and the beds set level,
+it will certainly, when under load, throw an extreme pressure upon that
+part of the bearing surface immediately under the forward edge of the
+bearing-plate. These considerations probably account for bedstones
+frequently cracking, in addition to which possibility there is the
+disadvantage that the designer does not know where the girder will rest,
+and cannot truly define the span. The variation of flange-stress due to
+this cause may, in a girder of ordinary proportions, having bearings
+equal in length to the girder's depth, be as much as 15 per cent. above
+or below that intended.
+
+If great care be taken in setting beds, in the first instance, to dip
+toward the centre of the span an amount depending upon the anticipated
+girder deflection, it may be possible to insure that when under full
+load the girder bearing shall rest equally upon its seat; but this is
+evidently a difficult condition to obtain practically, is good only for
+one degree of loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence of a
+slight leaning forward of abutment walls.
+
+Double or treble thicknesses of hair-felt are sometimes placed beneath
+girder bearings, with the object of securing a better distribution of
+pressure, no doubt with advantage; but this practice, though it may be
+quite satisfactory as applied to girders carrying an unchangeable load,
+hardly meets the case for loads which are variable. Notwithstanding the
+faulty nature of the plain bearing ordinarily used for girders of
+moderate span, its extreme simplicity commends it to most engineers. It
+must be admitted that no serious inconvenience need be anticipated in
+the majority of cases, particularly if the bearings are limited in
+length, do not approach nearer than 3 inches to the face of bedstones,
+and are furnished with hair-felt or similar packing.
+
+[Illustration: FIG. 1.]
+
+Whether with long or short bearings, the forward edge should be at right
+angles to the girder's length. In skew bridges it is sometimes seen that
+this edge follows the angle of skew. The effect on the girder is to
+twist it, as will be clear from a little consideration. In evidence of
+this the case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment right up to the
+masonry face at a rather bad angle (about 15 degrees), was, after twenty
+years, found canted over at the top to the extent of 4 inches, with the
+further result of springing a joint in the top flange at about the
+middle of the girder, causing some rivets to loosen. The bedstone was
+also very badly broken at the face, and had to be replaced in the course
+of repairs (Fig. 1). This girder had, in addition to the canting from
+the upright position at its end, and the distortion of the top flange, a
+curvature in the same direction, though less in amount, at the
+bottom--an effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder end to creep
+along the abutment away from the point at which it bears hardest, under
+frequent applications and removals of the live load, and accompanying
+deflections.
+
+This tendency to travel may be aggravated in bridges carrying a
+ballasted road, in which there may be a considerable thickness of
+ballast near the bearings, by the compacting and spreading of this
+material taking effect upon the girder end, tending to push it outwards,
+being tied only by a few light cross-girders badly placed for useful
+effect. The movement may be prevented in new work for moderate angles of
+skew by carrying the end cross-girders well back, and securing them in
+some efficient manner; or by the introduction of a diagonal tie
+following the skew face, and attached to cross and main girder flanges
+(Fig. 2)--a method which may be applied to existing work also.
+
+[Illustration: FIG. 2.]
+
+For such a case as that cited it is imperative that ballast pressure at
+the girder end should be altogether eliminated.
+
+The fixing of girder ends by bolts--a practice at one time usual--hardly
+calls for remark, as it is now seldom resorted to unless for special
+reasons; but it may be well to point out the weakening effect of holes
+for any purpose in bedstones. Bed-plates commonly need no fixing; the
+weight carried keeps them in position, or if, in the case of very light
+girders upon separate plates, it is considered well to secure these from
+shifting, it may best be done by letting the plate in bodily a small
+amount, or by means of a very shallow feather sunk into a chase.
+
+[Illustration: FIG. 3.]
+
+As an improvement upon the plain bearing usually adopted, it is an easy
+matter so to design girder-ends as to deliver the load by a narrow strip
+of bearing-plate carried across the bottom flange, distributing the
+pressure upon the stone, if there be one, by means of a simple
+rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle
+will by this means result, with freedom to slide, and the girder span be
+defined within narrow limits. A true knuckle is, of course, the best
+means of securing imposition of the load always in the same place; but
+this by itself is not sufficient where the girder is of a length to make
+temperature and stress variations important, in which case rollers, or
+freedom to slide, become necessary. Bridges exist in which
+roller-bearings have been adopted without the knuckle, or its
+equivalent, but this is wholly indefensible, as it is obvious that the
+forward roller will in all probability take the whole load, and cannot
+be expected to keep its shape and roll freely under this mal-treatment.
+It is sometimes asserted that rollers are never effective after some
+years' use; that they become clogged with dirt, and refuse to perform
+their office.
+
+There is no reason why rollers should not be boxed in to exclude dirt by
+a casing easily removed, some attention being given to them, and any
+possible accumulation of dirt removed each time the bridge is painted.
+
+To test the behaviour of rollers under somewhat unfavourable conditions
+for their proper action--that of the bearings of main roof trusses of
+crescent form, 190 feet span--the author, some thirty years since, took
+occasion to make the necessary observations, and found evidence of a
+moderate roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders resting upon
+columns, particularly if of cast iron, a roller and knuckle arrangement
+is most desirable for any but very small spans, as, if not adopted, the
+result will be a canting of the columns from side to side--a very small
+amount, it is true, but sufficient to throw the load upon the extreme
+edges of the base, though the knuckle alone will relieve the top of this
+danger. The author at one time took the trouble to examine, so far as it
+could be done superficially and without opening out the ground to make a
+complete inspection possible, a number of bridges crossing streets, in
+which girders rested upon and were secured to cast-iron columns standing
+in the line of kerb; and he found cracks, either at the top or bottom,
+in about one of every four columns.
+
+When girders passing over columns are not continuous, it may be
+difficult to find room for a double roller and knuckle arrangement; but
+this inconvenience may be overcome by carrying one girder-end wholly
+across the column-top, and securing the next girder-end to it in a
+manner which a little care and ingenuity will render satisfactory, one
+free bearing then serving to carry the load from both girders.
+
+Though the wisdom of using rollers is apparent in spans exceeding some
+moderate length, say 80 feet--as to which engineers do not seem quite
+decided--and varying with the conditions, it need not be overlooked that
+in some cases masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will yield a small
+amount without injury, and though shorter, if resting upon a bottom not
+absolutely rigid, will rock and give the necessary relief; but it is
+obvious, if the resistance to movement is sufficiently great, and the
+girder cannot slide or roll on its bearings, bedstones will probably
+loosen, as, indeed, frequently happens.
+
+
+
+
+CHAPTER II.
+
+MAIN GIRDERS; PLATE-WEBS.
+
+
+It is seldom that girders of this description--or, indeed, of any
+other--show signs of failure from mere defect of strength in the
+principal parts, even though somewhat highly stressed; and instances
+tending to support this statement will be given in a later chapter. For
+the present, it is proposed to indicate peculiarities of behaviour only,
+generally, but not always, harmless.
+
+Though now less often done, it was at one time common practice to load
+plate-girders on the bottom flange by simply resting floor timbers,
+rails, troughs, or cross-girders upon them. In outside girders one
+result of this is to cause the top flange to take a curve in plan,
+convex towards the road, every time the live load comes upon the floor
+of the bridge, upon the passing of which the flange resumes its figure,
+though still affected by that part of the load which is constant.
+
+A bridge of 47 feet span, carrying two lines of way, having one centre
+and two outside girders, with a floor consisting of old Barlow rails,
+resting upon the bottom flanges, showed the peculiarity named in a
+marked degree.
+
+The outside girders, under dead load only, were, as to the top flanges
+(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of
+straight in their length, but upon the passing of a goods engine and
+train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one
+outside girder, and 2-3/16 inches for the other.
+
+The centre girder, having a broader and heavier top flange, curved 5/8
+inch towards whichever road might be loaded. The effect of such
+horizontal flexure is clearly to induce stresses of tension and
+compression in the flanges, which, being (for the top flange) compounded
+with the normal compressive stress due to load carried, results in a
+considerable want of uniformity across the section.
+
+[Illustration: FIG. 4.]
+
+In the case under notice, the writer estimates the stresses for an outer
+girder top flange at 4�5 tons per square inch compression for simple
+loading, and 5�5 tons per square inch of tension and compression, on the
+inner and outer edges, due to flexure, resulting when compounded in a
+stress of 1 ton per square inch tension on the inside, and 10 tons per
+square inch compression on the outside edge. In this rather extreme case
+the stress on the inner edge, or that nearest the load, is reversed in
+character.
+
+The effect described appears to be not wholly due to the twisting
+moment. It is apparent that whatever curvature may be induced by
+twisting alone must be aggravated in the compression flange by its being
+put out of line.
+
+The writer does not attempt here to apportion the two effects in any
+other way than to say that the greater part of the flexure appears to be
+due to the secondary cause. Consistent with this view of the matter is
+the fact that the inclination of the girder towards the rails greatly
+exceeded the calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the floor rails
+bore hard at their extreme ends, at which point of bearing the
+calculated twisting moment accounts for less than one-half of the
+flexure observed in the flanges.
+
+[Illustration: FIG. 5.]
+
+The girders upon removal in the course of reconstruction again took the
+straight form, showing that the very frequent development of the
+stresses named had not sensibly injured the metal, though the bridge
+carried as many as three hundred trains daily in each direction, and had
+done so for very many years.
+
+The deformation of the top flange only has been noticed, yet the same
+tendency exists in the bottom, though the actual amount is much less,
+both because the lower flanges are in tension, and are also in great
+degree confined by the frictional contact of the cross bearers, even
+where no proper ties are used. In the case dealt with the bottom flanges
+of the outer girders curved 1/8 inch outwards only.
+
+With the broad flanges commonly adopted in English practice, twisting of
+the girders, under conditions similar to the above, will not generally
+be a serious matter; but with narrow flanges possessing little lateral
+stiffness it might be a source of danger.
+
+[Illustration: FIG. 6. FIG. 7.]
+
+The twisting may be limited in amount by introducing a cross-frame
+between the girders, from which they are stiffened; by strutting the
+girders immediately from the floor itself, in which case they cannot
+cant to a greater extent than that which corresponds to the floor
+deflection; or by designing the top flange to be unsymmetrical with
+reference to the web, as in Figs. 6 and 7, with the object of insuring
+that under the joint effect of vertical loading and twisting, the stress
+in the flange shall at maximum loads be uniform across the section, and
+allow it to remain straight. This may be secured by making the
+eccentricity of the flange section equal to that of the loading. For
+instance, if the load be applied 3 inches away from the web centre, the
+flange should have its centre of gravity 3 inches on the other side of
+the centre line. It can be shown that this is true throughout the length
+of the girder, and irrespective of the depth. An instance in which
+flange eccentricity being in excess, curvature outwards resulted, will
+be found in a later chapter on deformations, etc. It will not generally
+be necessary to make the bottom flange eccentric, as it is commonly tied
+in some way; but if done, the eccentricity should be on the same side as
+for the top. The flanges remaining straight under these conditions are
+not subject to the complications of stress referred to in the case first
+quoted. The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the kind
+discussed.
+
+It should be remarked that by the two first methods, if the stiffening
+frames are wide apart and attached direct to the web, there is a
+liability for this to tear, under distress, rather than keep the girder
+in line.
+
+There is one other possible consequence of throwing load upon the
+flanges of a girder of a much more alarming nature. In girders not very
+well stiffened, it may happen that the frequent application of load in
+this manner finally so injures the web-plate, just above the top edge of
+the bottom angle-bars, as to cause it to rip in a horizontal direction.
+More likely is this to happen with a centre girder taking load first on
+one side, then on the other, and again on both together. Cases may be
+cited in which cracks right through the webs 3 feet or more in length
+have resulted from this cause. It is very probable, however, that in
+some of these cases the matter was aggravated by the use of a poor iron
+in the webs, as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a girder, would,
+if they could not be made thin enough, even encourage the use of an
+indifferent metal as being quite good enough for that part of the work.
+
+An instance of web-fracture from somewhat similar causes may be here
+given.
+
+In a bridge of 31 feet 6 inches effective span, and consisting of twin
+girders carrying rails between, as shown in Figs. 8 and 9, the load
+resting upon the inner ledges, formed by the bottom flange, induced
+such a bending and tearing action along the web just above the
+angle-bars, as to cause a rip in one of the girders, well open for some
+distance, and which could be traced for 14 feet as a continuous crack.
+
+[Illustration: FIG. 8.]
+
+[Illustration: FIG. 9.]
+
+It will be noticed in the figure that the [T] stiffeners occur only at
+the outer face of the web, and that the inner vertical strips stop short
+at the top edge of the angles, the result being that under load the
+flange would tend to twist around some point, say A, at each stiffener,
+inducing a serious stress in the thin web at that place, while away from
+these stiffeners the web would be more free to yield without tearing.
+The fact that at a number of the stiffeners incipient cracks were
+observed, some only a few inches long, suggests this view of the matter.
+
+A case of web-failure from other influences coming under notice showed
+breaks at the upper part of the web extending downwards.
+
+In this bridge, of 32 feet span, which had been in existence thirty-two
+years, the webs--originally 1/4 inch thick--were, largely because of
+cinder ballast in contact with them, so badly wasted as to be generally
+little thicker than a crown-piece, and in places were eaten through; in
+addition to which, the road being on a sharp curve, the rail-balks had
+been strutted from the webs to keep them in position, the effect of
+which would be to exert a hammering thrust upon the face of the web at
+the abutting ends, and assist in starting cracks in webs already much
+corroded. A feature of this case, tending to show that the breaks
+resulted as the joint effect of waste and ill-usage by the strut
+members, rather than by excessive stress in the web as reduced, is to be
+found in the fact that the girders when removed were observed to be in
+remarkably good shape--i.e. the camber, marked on the original drawings
+to be 1-1/2 inch, still showed as a perfectly even curve of that rise,
+which would hardly have been the case if the lower flange had been let
+down by web-rupture, the result of excessive web-stresses.
+
+Occasionally webs will crack through the solid unwasted plate, in a line
+nearly vertical; not where shear stress is greatest, but generally at
+some other place, and from no apparent cause, either of stress or
+ill-usage. The writer has observed this only in the case of small
+girders not exceeding 2 feet in depth; and, for want of any better
+reason, attributes these cracks to poor material, coupled with some
+latent defect. In a bridge having some thirty cross-girders, each 26
+feet long, about every other one had a web cracked in this manner after
+many years' use.
+
+Web-cracks of the kind first indicated, are perhaps, the most probable
+source of danger in plate-girders, of any which are likely to occur. The
+fault is insidious, difficult to detect when first developed, and
+perhaps not seen at all till the bridge, condemned for some other
+reason, has the girders freely exposed and brought into broad light. The
+manner in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of these defects
+an uncertain matter, unless sufficient trouble is occasionally taken to
+render inspection complete.
+
+The manner in which girders with wasted and fractured webs will still
+hang together under heavy loading seems to warrant the deduction that,
+in designing new work, it can hardly be necessary to provide such a
+considerable amount of web-stiffening as is sometimes seen; experience
+showing that defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form of
+cracks.
+
+A case of web-buckling lies, so far, without the author's experience.
+There is no need to introduce, for web-stresses alone, more stiffening
+than that which corresponds to making the stiffeners do duty as vertical
+struts in an openwork girder; in which case it is sufficient to insure
+that the stiffeners occurring in a length equal to the girder's depth
+shall, as struts, be strong enough in the aggregate to take the whole
+shear force at the section considered, in no case exceeding this amount
+on one stiffener. For thin webs in which the free breadth is greater
+than one hundred and twenty times the thickness, the diagonal
+compressive stress may be completely ignored, and the thickness
+determined with reference to the diagonal tension stress only.
+
+There is one fault which frequently shows itself in stiffeners though
+not the result of web-stresses, and when performing an additional
+function--viz., the breaking of [T] stiffener knees at the weld, where
+brought down on to the tops of cross-girders, due to the deflection of
+the floor, as shown in Fig. 10. When such knees are used, the angle may
+properly be filled in with a gusset-plate to relieve the weld of strain
+and prevent fracture.
+
+[Illustration: FIG. 10.]
+
+There is some little temptation in practice to make use of the solid web
+as a convenient stop for ballast, or road material. Special means,
+perhaps at the cost of some little trouble, should be adopted, where
+necessary, to avoid this.
+
+
+MAIN GIRDERS; OPEN WEBS.
+
+With these, as with plate-girders, deficiency of strength--i.e. of
+section strength--is seldom so marked as to be a reasonable cause of
+anxiety. In particular instances faults in design may result in stresses
+of an abnormal amount, though rarely to an extent occasioning any ill
+effects. The practice of loading the bottom flanges at a distance from
+the centre, the bad effects of which have already been dealt with as
+applied to plate-girders, is not commonly resorted to in girders having
+open webs, nor are these so liable to be heaped with ballast in
+immediate proximity to essential members of the structure.
+
+Some defects are, however, occasionally seen which may be remarked. Top
+booms of an inverted [U] section are sometimes made with side webs too
+thin, and having the lower edges stiffened insufficiently, or not at
+all. Where this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to sustain the
+compressive stress to which the rest of the boom is liable. The practice
+of putting the greater part of the boom section in an outer flange,
+characteristic of this defect, has the further disadvantage of throwing
+the centre of gravity of the section so near its outer edge as to make
+impracticable the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section is thrown into
+the flange-plates, the centre of gravity of the section has no constant
+position along the boom--an additional inconvenience where correct
+design is aimed at.
+
+These considerations indicate the propriety of arranging the bulk, or
+all, of the section at the sides, thus reducing or getting rid of the
+objections named.
+
+Where the bottom boom consists of side plates, only one point demands
+attention. It is found that, though nominally in tension, the end bays
+are liable occasionally to buckle, as though under compressive stress,
+and need stiffening, not excepting girders which at one end are mounted
+on rollers. This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes, such as
+wind forces, or as in the case of a bridge carrying a railway, in which
+the rigidity of the permanent-way may be such that the bridge-structure,
+in extending towards the roller end, cannot move it sufficiently,
+causing a reversal of stress on the lighter portions of the bottom boom
+at the knuckle end; or by the exposed girder booms becoming very
+sensibly hotter than the bridge floor, and by expanding at a greater
+rate, cause this effect, from which rollers cannot protect them.
+
+In counterbracing consisting of flat bars it is desirable either to
+secure these where they cross other members, or stiffen them in some
+manner to avoid the disagreeable chattering which will otherwise
+commonly be found to occur on the passage of the live load.
+
+Occasionally diagonal ties are made up of two flat bars placed face to
+face, to escape the use of one very thick member. Where this is done,
+the two thicknesses, if not riveted together along the edges, will be
+liable to open, as the result of rusting between the bars in contact,
+when the evil will be aggravated by the greater freedom with which
+moisture will enter the space.
+
+Other matters relating to open-web girders will be more conveniently
+dealt with under their separate headings, particularly a further
+consideration of the relationship subsisting between the booms and floor
+structure.
+
+
+
+
+CHAPTER III.
+
+BRIDGE FLOORS.
+
+
+The floors of bridges commonly give more trouble in maintenance, and
+their defects are more frequently the cause which renders reconstruction
+necessary, apart from reasons not concerning strength, than any other
+part of such structures. When it is considered that this portion of a
+bridge is first affected by impact of the load which comes upon it, and
+is usually light in comparison with the main girders further removed
+from the load, and to which the latter is transferred through the more
+or less elastic floor, the fact will be readily appreciated by those not
+already familiar with it.
+
+The end attachments of cross and longitudinal girders are very liable to
+suffer by loosening of rivets, or, more rarely, by breaking of the
+angle-irons which commonly make such a connection. A not unusual defect
+of old work, which may also sometimes be seen in work quite new, where
+the cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends. There is
+small chance of these ever being properly tight, if the act of riveting
+is rendered difficult by bad design. This is the more objectionable if
+it happens that cross-girder ends abut against opposite sides of the web
+of an intermediate main girder, and are secured by the same rivets
+passing through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which they become
+subject, as the cross-girders take their load and deflect under it,
+will be very apt to loosen them. The author has seen a case of this kind
+(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the
+whole of the cross-girder end rivets were loose, some nearly worn
+through, thus allowing the cross-girders to be carried, not by their
+attachments, but by resting upon the main-girder flanges, which in turn,
+by repeated twisting, tore the web for a length of 4 feet; there was
+also pronounced side flexure of the top booms. The movements generally
+on this bridge (of 42-feet span), whether of main or cross-girders, were
+very considerable and disturbing. It was removed after about
+twenty-three years' use.
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+There is no necessity, as a rule, for the ends of cross-girders attached
+to the same main girder at opposite sides to be placed in line. The
+author prefers to arrange them to miss, by which device each connection
+is entirely separate, the riveting can be more efficiently executed,
+erection is simplified, and the rivets will be more likely to keep
+tight. Other special cases of cross-girder ends will be dealt with under
+the head "Riveted Connections."
+
+It is sometimes contended that cross-girders attached at their ends by a
+riveted connection should be designed as for fixed ends, in which case
+they are usually made of the same flange section throughout, with a view
+to satisfy the supposed requirements. But a girder to be rightly
+considered as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction, and no
+overhead bracing, this is so far from being the case as to leave little
+occasion for taking the precaution named. As the cross-girders deflect,
+the main girders will commonly yield slightly, inclining bodily towards
+the cross-girders, if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in this manner is
+usually less than that which corresponds to fixing the cross-girder
+ends, and is, generally, slight. It is, of course, necessary that this
+measure of resistance at the connection should be borne in mind for the
+sake of the joint itself, quite apart from any question of fixing.
+
+Possibly, in quite exceptional cases, where very stiff main girders are
+braced in such a manner as to prevent canting, it may be proper to
+consider the cross-girder ends as fixed, or for those near the bearings
+of heavy main girders; but the author has not met with any example where
+cross-girders, apart from attachments, appear to have suffered from
+neglect of this consideration.
+
+With cross-girders placed on either side of a main girder, and in line,
+it may also, for new work, be desirable to regard the ends as fixed, and
+to detail them with this in view. It does not, however, appear wise to
+carry this assumption to its logical issue, and reduce the flange
+section to any appreciable extent on this account. The fixity of the
+ends will, in any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a moderate effect in
+reducing flange stress at the middle of the loaded floor beam.
+
+[Illustration: FIG. 13. FIG. 14. FIG. 15.]
+
+Similar reasons affect the design of longitudinal girder attachments to
+cross-girders, which, if intended to support rails, cannot of necessity
+be schemed to come other than in line. Where the floor is plated as one
+plane surface, there will not usually be any trouble resulting if no
+special precautions are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving the
+joints of abnormal stress. If the plating is, however, designed in a
+manner which does not present this advantage, or if the floor be of
+timber, it is better to decide whether the connections shall be
+considered as fixed, and made so; or avowedly flexible, and detailed in
+such a manner as to possess a capacity for yielding slightly without
+injury. Those connections are most likely to suffer which are neither of
+the one character nor the other, offering resistance without the ability
+to maintain it. Figs. 13, 14, and 15 give representations of three
+"spring joint" methods of insuring yield in a greater or less degree.
+For small longitudinals it is, perhaps, sufficient to use end angles
+with very broad flanges against the cross-girder web; these to be
+riveted in the manner indicated in Fig. 15.
+
+Liberal depth to floor beams is distinctly advantageous where it can be
+secured, rendering it easier to design the ends in a suitable manner, by
+giving room near mid-depth of the attachment to get in the necessary
+number of rivets; or where the ends are rigidly attached direct to
+vertical members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with a
+correspondingly reduced cant of the main girders and flexure of the
+vertical member, with smaller consequent secondary stresses. In any case
+deep girders will contribute to stiffness of the floor itself,
+favourable in railway bridges to the maintenance of permanent-way in
+good order.
+
+[Illustration: FIGS. 16, 17, 18.]
+
+A point in connection with skew-bridge floors occasionally overlooked is
+the combined effect of the skew, and main girder camber, in throwing the
+floor structure out of truth, if no regard has been paid to this. The
+result is bad cross-girder or other connections; or, in the case of
+bearers running over the tops of main girders, a necessity for special
+packings to bring all fair (Fig. 17). The author has in such cases,
+where cross-girders are used, set the main girder beds at suitable
+levels, in order that the cross-bearers may all be horizontal (see Figs.
+16 and 18). This may not always be permissible; but, however the
+difficulty may be met, it should be dealt with as part of the design.
+For small angles of skew only may it be neglected.
+
+Rivets attaching cross-girder angles to the web will occasionally
+loosen, probably due in most cases to bad work, together with some
+circumstance of aggravation, as in the case of a bridge floor consisting
+of girders spaced 3 feet 6 inches apart, with short timber bearers
+between, carrying rails. In many girders the top row of rivets, of
+ordinary pitch and size, had loosened, allowing the web, about 1/4 inch
+thick, a movement of 1/8 inch vertically. The rails being very close
+down upon the cross-girder tops, though not intended to touch, had at
+some time probably done so, and by "hammering" produced the result
+described.
+
+Plated floors are often found which are objectionable on account of
+their inability to hold water, arising sometimes from bad work, as often
+from wide spacing of rivets. With rivets arranged to be easily got at,
+and pitched not more than 3 inches apart, a tight floor may be expected;
+but it is still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside of the
+plate, and sufficiently long to deliver direct into gutters, where these
+are necessary. Drain-holes should not be less frequent than one to every
+50 square feet of floor, if flat, and may advantageously be more so.
+Gutters should slope well, and care be taken to insure practicable
+joints and good methods of attachment--a matter too often left to take
+care of itself, with considerable after-annoyance as a result.
+
+The use of asphalt, or asphalt concrete, to render a plated floor
+water-tight is hardly to be relied upon for railway bridges, though no
+doubt effective for those carrying roads. It is extremely difficult to
+insure that it shall stand the jarring and disturbance to which it may
+be subject, and under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying of the floor.
+In bulk, as in troughs, it may be useful, but in thin coverings on
+plates it cannot be depended upon.
+
+Floors having plated tops are sometimes finished over abutments or piers
+in a manner which is not satisfactory, either as regards the carrying of
+loads or accessibility for painting. If the plates are carried on to a
+dwarf wall with the intention that the free margin of the plate shall
+rest upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after the girder work
+is in place, making it difficult to insure that the wall really supports
+the plate, the result being that this may have to carry itself as best
+it can. In any case, severe corrosion will occur on the underside, and
+the plate rust through much before the rest of the floor; the masonry
+also will usually be disturbed.
+
+It appears preferable to form the end of the floor with a vertical
+skirting-plate having an angle or angles along the lower edge. This may
+come down to a dwarf wall, but preferably not to touch it, the skirting
+being designed to act as a carrying girder. A convenient arrangement is
+shown in Fig. 19, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the skirting
+referred to being carried continuously along the floor edge, and
+attached to each girder-web, the whole of the more important parts being
+open to the painter.
+
+[Illustration: FIG. 19.]
+
+Trough floors consisting of one or other of the forms of pressed or
+rolled section present the objection that it is almost impracticable to
+arrange an efficient connection at the ends, if they abut against main
+girders, and but little connection is, as a rule, attempted, and
+sometimes none. The result is that the load from these troughs is
+delivered in an objectionable manner, and the ends being open or
+imperfectly closed, water and dirt escape on to the flange, or other
+ledge, which supports them. A description of pressed floor which
+promises to overcome this objection, and provide a ready means of
+attachment to the webs of plate-girders, or of booms having vertical
+plate-webs, has within the last few years been introduced. This has the
+ends shaped in such a manner as to close them and provide a flat surface
+of sufficient area for connection by rivets. Each hollow is separately
+drained by holes with nozzles. Whether this type of trough will develop
+faults of its own, due to over-straining of the metal in the act of
+pressing, remains to be seen; but as it appears possible to produce the
+desired form without any material thinning or thickening of the metal,
+the contention that no severe usage accompanies the process appears to
+be reasonable.
+
+That form of troughing in which the top and bottom portions are
+separately formed, and connected by a horizontal seam of rivets at
+mid-depth, is found in use upon railway bridges to be very liable to
+loosening of those rivets near the ends; less surprising, perhaps,
+because the sloping sides are usually thin.
+
+It is a distinctly difficult matter to join two or more lengths of any
+trough flooring having sloping sides, in a workmanlike manner; the fit
+of covers is apt to be imperfect, and some rivets, being difficult of
+access, are likely to be but indifferently tight, so that if the joint
+occurs where it will be more than lightly stressed, trouble will
+probably follow. A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most severe, any
+leakage come directly upon the girder, and remedial measures be more
+difficult to carry out.
+
+Timber floors of the best timber, close jointed, are more durable than
+might be supposed. The disadvantage is a difficulty in ascertaining the
+precise condition of the timber after many years' use. The author has
+seen timbers, 9 inches by 9 inches, forming in one length a close floor,
+carried by three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces with the
+foot; whilst in another case, with the same arrangement of girders and
+close-timbered floor, the wood, after being in place for thirty-two
+years, was, when taken out, found to be perfectly sound, with the
+exception of a very few bad places of no great extent. In this instance,
+however, it is known that the floor--pitch-pine--was put in by a
+contractor who prided himself upon the quality of the timber that he
+used; the floor being also covered with tar concrete, which had in this
+instance so well performed its office as to keep the timber quite dry on
+the top.
+
+Jack arches between girders make an excellent floor for road bridges,
+though heavy; and for small bridges may be used to carry rails, if the
+girders are designed to be stiff under load. The apprehension that
+brickwork or concrete will separate from the girder-work, or become
+broken up under even moderate vibration, does not seem to be well
+founded, if the deflection is small and the brickwork or concrete good.
+
+The use of corrugated sheeting as a means of rendering the underside of
+a bridge drop dry cannot be too strongly deprecated. If it must be
+adopted, the arrangement should be such as to permit ready removal for
+inspection and painting. It is evident that by boxing up the floor
+structure, rust is favoured, and serious defects may be developed, not
+to be discovered till the sheeting is removed, or something happens.
+
+[Illustration: FIG. 20.]
+
+A case may be instanced in which it was found, on taking down sheeting
+of this description, that the floor girders, previously hidden, were
+badly wasted in the webs. One of these girders had cracked, as shown in
+Fig. 20, and others were in a condition only less bad.
+
+In any floor carrying ballast or macadam, if means are not adopted to
+keep the road material from the structure of the floor, or from the main
+girders, corrosion may be serious in its effects. Cinder ballast is,
+perhaps, the worst in this respect, in its action upon steel or
+ironwork, being distinctly more damaging than any other kind commonly
+used.
+
+Rail-joints upon bridge floors are to be avoided where practicable by
+the use of rails as long as can be obtained; if the bridge is small
+enough, crossing it in one length. At each joint there is likely to be
+hammering and working extremely detrimental to floor members and
+connections; indeed, it may happen that loose rivets will be found in
+the neighbourhood of such joints, and nowhere else on the bridge. Where
+rail-joints cannot be avoided, their position should, if there be any
+choice, be judiciously selected, and the plate-layers taught to close
+the joints and jam the fish-bolts.
+
+[Illustration: FIG. 21.]
+
+As rail-joints upon a bridge may injuriously affect the floor, so also
+will a weak floor be very trying to the rails. A remarkable instance of
+this has come under the writer's notice, where a bridge (Fig. 21) of
+three 33-feet spans, having outer and centre main girders, with
+cross-girders spaced 3 feet apart, resting upon the girder flanges, but
+not attached, and carrying two roads, had the permanent-way in a very
+bad state. The rails proper, with supplementary angle-plates, rested
+direct upon the cross-girders, which were decidedly light, and the whole
+floor had much "life" in it, the ill-effect of which was shown in
+thirteen breaks in the angle-plates, in each case near their ends,
+generally at holes.
+
+It appears probable that severe stresses may be thrown upon the parts of
+a floor, whether placed at the level of the bottom booms or of the top,
+by changes of length in the booms due to stress. The author has,
+unfortunately, no direct evidence to offer in reference to this, tending
+either for or against the contention. If an unplated floor of cross and
+longitudinal girders of usual arrangement be at the bottom boom of a
+large bridge, as the boom lengthens with the imposition of load upon the
+bridge, all the cross-girders from the centre towards the abutments will
+be curved horizontally, the middle portion being restrained by the
+longitudinals from moving bodily with the ends. Each cross-girder except
+that at the centre, if there be one, will thus present a figure in plan,
+concave towards the abutment to which it is nearest. This will be
+accompanied by stressing of the connections, and a transfer to the
+longitudinals of as much of the tensile stress properly belonging to the
+booms as the stiffness of the cross-girders may communicate.
+
+This in itself will hardly be considerable, and will be the less on
+account of a slight yielding which may be expected at the end
+connections of each longitudinal; but the effect upon the cross-girders
+by horizontal bending will be much marked. If the case be supposed of a
+200-feet span in steel at ordinary loads and stresses, carrying one line
+of way, with cross-girders 20 feet apart, and having no floor-plates, it
+may be ascertained, neglecting for the moment any slight yielding of the
+longitudinal girder connections, that upon the bridge taking its full
+live load there will be the following approximate results: Movement at
+each end of the end cross-girders of 3/10 inch, equivalent to a force of
+7-1/2 tons, tending to bend them horizontally, and a mean stress on the
+outer edges of the girders, 12 inches wide, of 8 tons per square inch
+due to flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge, of
+3/4 ton per square inch. Normal elongation of the longitudinal girder
+bottom flanges, and compression of the top, modifies the figures
+unfavourably as to the cross-girder top flange. Yielding of the
+connections named before has been neglected in arriving at these
+stresses. If they are sufficiently accommodating to give freely, to a
+mean extent, as between the top and bottom of each joint, of 1/29 inch,
+these results will disappear. It is evident, however, that we cannot
+rely upon good work yielding without the existence of considerable
+forces to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.
+
+The most favourable case has been taken; if now it is assumed that the
+floor has continuous plating, the results would seem to be much more
+astonishing. It will appear on this supposition that the boom stresses,
+instead of being taken wholly by the booms, are about equally divided
+between these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which for the end
+cross-girders will approach 40 tons at each connection--considerably
+more than the vertical reaction under normal loads.
+
+Palpably, these conclusions must be greatly modified by the yield of
+longitudinal girder ends, and slip of the floor rivets in transverse
+seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the
+stress at each, as estimated, would be sufficient to induce shear of
+about 6 tons per square inch--more than enough to cause "slip." After
+making this allowance, it is still evident there must be very serious
+forces at work about the ends of cross-girders under the conditions
+supposed, probably not less than one half the amounts named, as with
+this reduction the floor rivets should not yield, given reasonably good
+work. It is to be observed that the effect of live load only has been
+introduced, on the presumption that the longitudinals and floor-plating
+have not been riveted up till the main girders have been allowed to
+carry the major part of the dead load; but even this cannot always be
+conceded. The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these possible
+effects, either with the object of rendering the communication of these
+forces harmless, or making the floor so that it shall take little or no
+stress from the main booms, by arranging joints across the floor
+specially designed to yield, the ends of longitudinals being schemed
+with the same object. Where there is no plating, the case is, perhaps,
+sufficiently provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these girders
+upon the top of the cross-girders, when stretching of the bottom flanges
+of the rail-bearers under load may be expected, within a little, to keep
+pace with the lengthening of the main booms.
+
+It would appear that light pressed troughs running across the
+longitudinals would, by yielding in every section, also furnish relief,
+as compared with the rigidity of flat plates.
+
+By placing the floor at a level corresponding to the neutral axis of the
+main girders, the communication of stress to the floor may be avoided;
+but it seldom happens that there is so free a choice as to floor height
+relative to the girders. This solution is, therefore, of limited
+application.
+
+It is obvious that somewhat similar effects must obtain to those
+considered in detail, when the floor structure lies at the level of top
+booms, but with forces of compression from the booms to deal with,
+instead of tension.
+
+
+
+
+CHAPTER IV.
+
+BRACING.
+
+
+Bracing, whether to strengthen a structure against wind, to insure the
+relative positions of its parts, or for any other purpose, cannot be
+arranged with too great care and regard to its possible effects. Forces
+may be induced which the connections will not stand, with loose rivets
+as a consequence, and inefficiency of the bracing itself; or, the
+connections holding good, stresses in the main structure may, perhaps,
+be injuriously altered.
+
+To take a not uncommon case, let us suppose a bridge consisting of four
+main girders placed immediately under rails of ordinary gauge, and
+braced in vertical planes only, right across from one outer girder to
+the other. If the roads were loaded always at the same time, nothing
+objectionable would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and deflects, the bracing
+under the six-foot will endeavour to communicate some part of this load
+to the other pair of girders. If the bracing is so designed that some
+correctly calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections, there
+will be no harmful consequences; but if not, the bracings will most
+probably work at the ends; this, indeed, is what frequently happens.
+There is one other effect which will ensue, if the bracing is wholly
+efficient; a certain twisting movement of the bridge will occur, which
+increases the live load upon the outer girder on the loaded side of the
+bridge to the extent of 10 per cent., with a corresponding lifting force
+at the outer girder on the unloaded side. These amounts are not serious,
+but wholly dispose of any advantage it is conceived will be gained by
+causing the otherwise idle girders to act through the medium of the
+bracing. In road bridges of similar arrangement, over which heavy loads
+may pass on any part of the surface, it is clear that the use of bracing
+between girders should not be taken as justifying the assumption that
+the load is distributed over many girders, and correspondingly light
+sections adopted, unless the effect of twisting on the whole bridge is
+also considered, and justifies this view; for, as already stated in the
+case of the railway bridge, the net result may be to increase the girder
+stresses instead of reducing them. Generally, it may be deduced that the
+better plan for railway bridges is to brace the girders in pairs,
+leaving, in the case supposed, no bracing between the two middle
+girders, though there will be no objection to connecting these by simple
+transverse members of no great stiffness, to assist in checking lateral
+vibration. For road bridges of more than five longitudinal girders,
+equally spaced, it may be advantageous to brace right across, the
+twisting effect with this, or a greater, number of girders not, as a
+rule, leading to any increase of load on any girder. Figs. 22 to 25 give
+the distribution of live load, placed as shown, for 3, 4, 5, and 6
+girders.
+
+It is to be observed that these statements do not apply to cases where
+there may be also a complete system of horizontal bracing, the effect of
+which, in conjunction with cross diagonals, may be greatly different,
+with considerable forces set up in the bracing, and a modification of
+girder stresses.
+
+These effects may be so considerable as to call for special attention in
+design where such an arrangement is adopted.
+
+[Illustration: FIG. 22.]
+
+[Illustration: FIG. 24.]
+
+[Illustration: FIG. 23.]
+
+[Illustration: FIG. 25.]
+
+Somewhat similar straining to that first indicated may occur in bracings
+placed between the girders of a bridge much on the skew. If this is, on
+plan, at right angles to the girders, as is commonly and properly the
+case, the ends will evidently be attached to the girders at points on
+their length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts, and the
+bracing will, if at one end attached near a rigid bearing, transfer some
+part of the load from one girder to the other, notwithstanding that
+both girders may be of the same span and equal extraneous loading. It
+would not be difficult to ascertain the amount of load so transferred
+from a consideration of the relative movements if free, and the loads on
+the two girders necessary to render these movements equal, if the
+deflections were simply vertical; but as there will be some twisting and
+yielding of the girders on their seats, the calculation becomes
+involved. If the bracing is placed at about the middle of the girders,
+the effects noted will be greatly reduced; first, because the difference
+of movements near the centre will be less; second, any given difference
+will correspond to a smaller transference of load; and, third, because
+each girder will there be more free to twist than at the ends. It
+therefore appears that bracings between the girders of a skew bridge
+should not be placed near the bearings, though they may be put, with
+much less risk of injury, near the middle.
+
+Cross-girders on a skew bridge are subject to forces somewhat similar to
+those which may affect bracing, rendering it desirable to design their
+attachments in a manner which shall not aggravate the matter, but rather
+reduce the effects of unequal vertical displacement of their ends where
+secured to the main girders.
+
+Crossed flat bars as bracing members are objectionable on account of
+their tendency to rattle, after working loose; but as this effect only
+ensues in bracing which has first become loose (it being assumed that
+the bars in any case are connected where they cross), this objection is
+not itself vital, though greater rigidity is easily obtained by making
+all such members of a stiff section.
+
+Defective bracing between girders, from neglect of the very considerable
+forces it may be called upon to communicate, is very common; the writer
+has seen many such cases, of which one is here illustrated in Fig. 26.
+
+[Illustration: FIG. 26.]
+
+This bridge, of the section shown, and 85 feet span, had very light web
+structure. The bracings, of which there were two sets, were wholly
+inefficient, the end rivets being loose in enlarged holes. Upon the
+passage of a train there was a positive lurching of the girder tops from
+side to side. The integrity of the bridge was really dependent upon
+such stiffness as there was in the girders, and unplated floor.
+
+A common but indifferent method of keeping the top members of main
+girders in line is by the use of overhead girders alone, frequently
+curved to give the requisite clearance over the road. This cannot be
+considered as wholly inefficient, as sometimes maintained, since it is
+evident that the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must take a greater
+force to distort it than would be necessary to cause deformation of a
+corresponding degree, in an open frame formed by the omission of the
+overhead girder; but it is not a method to be recommended, its precise
+utility is difficult to estimate, and, if the cross-girder attachments
+are of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however, not applicable
+to this arrangement alone. All overhead bracing favours this by
+restraining the tendency of the top booms to cant inwards when the floor
+beams are loaded; and though this restraint may be quite harmless, it is
+desirable that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in its character.
+"Sway" bracing, sometimes introduced at right angles to the bridge
+between opposite verticals, tends to emphasise these effects by
+rendering the cross-section of the bridge still stiffer, besides making
+it a matter of difficulty to ascertain how much of the wind forces on
+the top boom is carried to the abutment by the top system of bracing,
+and how much by the floor. The author does not, however, mean to suggest
+that it cannot be used with propriety, but rather that extreme care is
+desirable in considering its ultimate effect on the rest of the
+structure.
+
+For girders of moderate depth there may be on these grounds a distinct
+advantage in abandoning overhead bracing, and securing rigidity of the
+top boom, and adequate resistance to wind forces, by making the
+connection between the cross-girders and the web members sufficiently
+good to insure, as a whole, a stiff [U]-shaped frame; but this, with the
+ordinary type of rocker arrangement under the main girder bearings, will
+not be entirely free from objection, as canting of the girders due to
+floor loading will throw extreme pressure on the inner end of each
+rocker. There appears to be no reason why the cylindrical knuckle should
+not in this case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.
+
+[Illustration: FIG. 27.]
+
+The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom flanges,
+renders very narrow top booms permissible. This is a decided advantage
+where lightness of appearance is aimed at; but it is not unusual to see
+an attempt made in this direction by introducing gusset plates of very
+ample proportions between vertical members of the girders, and the
+projecting ends of flimsy transoms, carried beyond the width of the
+bridge proper, these being of a section wholly out of proportion to the
+brackets they are supposed to secure. Whatever may be the amount of
+strength necessary at the point A, in Fig. 27, there should not be less
+throughout the transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the vertical
+stiffeners is not, as a rule, great. Information to enable this question
+to be dealt with as a matter of calculation is somewhat scanty; but it
+would appear to be sufficient to insure safety that, for an assumed
+small amount of curvature in the compression member, the forces outwards
+corresponding to this curvature, due to thrust, should be resisted by
+verticals and transoms of strength and stiffness sufficient to restrain
+it from any further flexure. It will, of course, be necessary also to
+take care that the compression member is good as a strut between the
+points of restraint. A simple and sufficiently precise method of dealing
+with this question is much needed. In cases where the floor weight rests
+on the flange projection, it is also necessary to give the transom
+additional strength to an extent enabling it to resist the twisting
+effort between any two of these transverse members; further, resistance
+to wind on the girder has to be provided in both transoms and verticals.
+
+It may be hardly necessary to insist that bracing intended to stiffen a
+structure against wind, local crippling, or vibration, should be made
+complete, not stopping short at some point, because it cannot
+conveniently be carried further, as is sometimes done, unless the
+strength of those parts of the structure through which the forces from
+the bracing must be communicated to the abutments is sufficiently great,
+considered with reference to other stresses in those parts which have
+also to be endured.
+
+Bracing stopped short in this way, making only the central part of a
+bridge rigid, may have the effect of increasing the forces to which the
+unstiffened end members would otherwise be liable. Such a structure
+would evidently be much stiffer against wind-gusts than if no bracing
+existed--the resistance to a blow would be increased; but the power to
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater maximum forces than
+if bracing were wholly omitted. The net effect may still be better than
+with no bracing, the point raised being simply that of an increase of
+stress in particular end members.
+
+In the bracing of tall piers, the rising members of which will be
+subject to any considerable stress, if the diagonal members are not
+finally secured when the piers are under their full load, or an initial
+stress of proper amount induced in those members, the effect of loading
+will be to render them slack; so that an appreciable amount of movement
+at the top may occur before it can be limited by the efficient action of
+the bracings. This effect under blasts of wind or continual passage of
+trains may, indeed, be dangerous. Similar considerations apply to the
+top wind bracing of deep girder bridges, influencing also the bottom
+bracing in a contrary manner, which calls for attention in fixing the
+unit stresses for such members.
+
+The bracing of sea-piers is very liable to slacken if made with
+pin-and-eye ends, as is often done for round rods. The detail presents
+advantages in erection, but is not altogether satisfactory in practice.
+Such connections are continually working. In the finest weather, with
+the sea quite smooth but for an almost imperceptible wave movement, the
+lower parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there room for
+surprise when it is considered that these oscillations, occurring at
+about ten to each minute, never wholly cease, and amount in the course
+of one year to over five million in number.
+
+Bracing attached in such a manner that there can be no initial slack, or
+slack due to wear under endless repetitions of small amounts of stress,
+will have a much better chance to keep tight. The advantage presented
+by round rods in offering little surface to the water, is more than
+negatived by inefficiency of the usual attachments for such rods.
+
+The author has observed that bracing of members possessing some
+stiffness, and with good end attachments to ample surfaces, appears to
+stand best in ordinary sea-pier work. For such structures the bracing
+should consist of a few good members, with a solid form of attachment,
+rather than of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very possibly also, in
+the case of sea-pier work, in unskilled hands. If round rods must be
+used, they will stand much better if made of large diameter.
+
+Before leaving the subject of bracing, it may not be out of place to
+refer to wind pressure, as this may so much affect the proportioning of
+the members.
+
+Some years since the author had occasion to examine a number of
+structures with respect to their stability. Of foot-bridges from 60 feet
+to 120 feet long, three or four, when calculated on the basis
+recommended by the Board of Trade as to pressures upon open-work
+structures, worked out at an overturning pressure of from 18 lb. to 22
+lb. per square foot. These bridges had been many years in existence; it
+is, therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them as to the
+whole surface.
+
+[Illustration: FIG. 28.]
+
+Particulars were taken in 1895 of a notice-board, presenting about 12
+square feet of surface, which was blown down in the great storm of March
+24 of that year, at Bilston, in Staffordshire. It was situated at the
+foot of a slight slope, over which the wind came, striking the
+obstruction at right angles. The board was mounted on two oak posts of
+fair quality and condition, which broke near the ground at bolt holes
+(see Fig. 28). The force required to do this, at 9000 lb. modulus of
+rupture--a moderate value--corresponds to 50 lb. per square foot on the
+surface exposed above the break.
+
+In the same neighbourhood, at the same time, considerable damage was
+wrought in overturning chimney stacks, to buildings and roofs; the
+general impression in the locality being that the storm was of
+exceptional, even unprecedented, violence. Bilston, it should be noted,
+lies high.
+
+At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27
+lb. was registered. In another part of the country it is said to have
+been 37 lb. Wind is so capricious in its effects over small areas as to
+render it probable that the maximum pressures have never been recorded;
+but this is a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by themselves
+insufficient to throw much light on the question, may be of use in
+connection with other known examples.
+
+
+
+
+CHAPTER V.
+
+RIVETED CONNECTIONS.
+
+
+Considerable latitude is observable in the practice of engineers in the
+use of rivets. Numberless experiments to determine the resistance of
+riveted connections have from time to time been made, but these are not
+to be considered by themselves as final, when the results of experience
+in actual construction, are available for further enlightenment.
+
+The class of workmanship so largely influences the degree in which
+rivets will maintain their integrity that it is only by the observation
+of a large number of cases, including all degrees of workmanship, that
+any reliable conclusions may be drawn. In this respect laboratory
+experiments have an apparent advantage, as the conditions may be kept
+sensibly the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must in the end
+determine the utility of any inquiry for practical application.
+
+The author has studied the particulars of a number of cases to ascertain
+under what conditions as to stress, having due regard to the effects of
+vibration, rivets will remain tight, or become loose. Every loose rivet
+that may be found cannot, of course, be taken as being due to excessive
+stress; the more frequent cause is indifferent work, evidenced by the
+fact that neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon the
+remainder. When rivets loosen as the direct result of over-stress, it is
+usually by compression of the shank and enlargement of the hole, or by
+stretching of the rivet and reduction of its diameter. Instances of
+failure by partial or complete shear are extremely rare; indeed, the
+author has never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work, it is not
+uncommon to find it cut or bent as an after consequence.
+
+In estimating stresses at which rivets have remained tight, or loosened,
+as the case may be, examples have generally been chosen in which there
+could be no reasonable doubt as to the amount of those stresses by the
+ordinary methods of computation. This is clearly most important, as, if
+any appreciable uncertainty remained as to the degree of stress, the
+results deduced would be of little value. For this reason those
+instances in which the loads upon girders, or parts of girders, may find
+their way to the supports by more than one route, are to be regarded
+with caution, as are those in which full loading possibly never obtains,
+but which may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been used in
+making the computations; in some cases from direct measurement from
+particular rivets, in others with a suitable allowance for excess
+diameter of hole, according to the class of work under consideration.
+
+Dealing first with main girders, it may be said that rivets attaching
+the webs of plate girders to the flange angles rarely loosen, though
+subject to considerable stress. In illustration of this may be named a
+bridge for two lines of way, 85 feet effective span, having two main
+girders with plate webs, and cross-girders resting on the top flanges,
+previously referred to (see Fig. 26).
+
+The girders, which were 6 feet 9 inches deep, had a bearing upon the
+abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches
+pitch. There is in a case of this kind some little uncertainty as to
+what is the stress on the flange angle rivets at, or very near to, the
+bearings; but, taking the vertical rows of rivets at the web joints near
+the ends as presenting less uncertainty, the stress per rivet works out
+at 4�8 tons, being 4 tons per square inch on each shear surface, and 11
+tons per square inch bearing pressure upon the shank in the web plate,
+which was barely 1/2 inch thick. This bridge was frequently loaded upon
+both roads, but with one road only carrying live load, the stresses in
+the more heavily loaded girder would be fully 90 per cent. of those
+obtaining as a maximum. There was on this bridge, which had been in use
+31 years, considerable movement and vibration.
+
+It is by no means uncommon to find cases of rivets in main girders
+taking 11 tons per square inch bearing pressure--occasionally more--and
+remaining tight. As furnishing an instructive, though slightly
+ambiguous, instance of rivets in single shear, may be cited a bridge not
+greatly less than that just referred to, of about 65 feet span, carrying
+two lines of way, there being two outer and one centre main girder of
+multiple lattice type, with cross-girders in one length 4 feet apart,
+riveted to the bottom booms of the main girders; these rivets, by the
+way, were in tension. The floor was plated, the road consisting of stout
+timber longitudinals, chairs, and rails (Fig. 29).
+
+[Illustration: FIG. 29.]
+
+It should be noted that there is in this case some difficulty in
+ascertaining the precise behaviour of the cross-girders, affecting the
+proportion of load carried by the outer and the inner main girders.
+Strict continuity of all the cross-girders could only obtain if the
+deflection of the main girders were such as to keep the three points of
+suspension of each cross-girder in the same straight line. A close
+inquiry showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would, under load,
+by relative depression of the middle point of support, be reduced to
+the condition of two simple beams, those at the extreme ends of the span
+would behave as continuous girders.
+
+With both roads carrying engine loads equal to those coming upon the
+bridge, the author estimates that for the centre main girder the shear
+on the rivets of the end diagonals, secured by one rivet only, was 14�9
+tons per square inch, and the bearing pressure 16�3 tons; the flange
+stress being 7�1 tons per square inch net. The outer main girders are
+most heavily stressed when but one road, next to the outer girder
+considered, carries live load. For this condition the stresses work out
+at 9 tons per square inch shear on the rivets of the end diagonals, and
+9 tons bearing pressure, the flange stress being 5�7 tons per square
+inch on the net section.
+
+Without intending to throw any doubt upon the substantial truth of these
+results, it must be admitted that instances of greater simplicity of
+stress determination are much to be preferred. For purposes of
+comparison, but not as having any other value, the results have also
+been worked out on the supposition of all cross-girders acting each as
+two simple beams, and also for strict continuity, and are here
+tabulated, together with the conclusions given above.
+
+The cross-girders were moderately stressed, and the tension on the
+rivets attaching them to the main girders probably did not exceed 3 tons
+per square inch.
+
+It should be pointed out that the traffic over the bridge was small. The
+centre main girder but seldom bore its full load, though at all times
+liable to receive it. Much importance cannot, therefore, be attached to
+the results for this girder, other than as showing how a structure may
+stand for many years, though liable at any time to the development of
+stresses which would commonly be regarded as destructive, or nearly so.
+
+EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS.
+
+  ---------------------------------+-----------+------------+---------
+                                   |   Cross-  |   Cross-   |
+                                   |  Girders  | Girders as | Correct
+                                   | as Simple | Continuous | Results.
+                  --               |   Beams.  |   Beams.   |
+                                   +-----------+------------+---------
+                                   | Stress in Tons per Square Inch.
+  ---------------------------------+-----------+------------+---------
+  Centre girder, 63 ft. span (both |           |            |
+  roads loaded):                   |           |            |
+    Rivets in diagonals--Shear     |    13�7   |    17�2    |  14�9
+          Do.            Bearing   |           |            |
+                         pressure  |    15�0   |    18�8    |  16�3
+                         Flange    |           |            |
+                         stress    |     6�8   |     8�5    |   7�1
+                                   |           |            |
+  Outer girder, 66 ft. span (near  |           |            |
+  road loaded):                    |           |            |
+    Rivets in diagonals--Shear     |     9�6   |     8�2    |   9�0
+          Do.            Bearing   |           |            |
+                         pressure  |     9�6   |     8�2    |   9�0
+                         Flange    |           |            |
+                         stress    |     5�9   |     5�1    |   5�7
+  ---------------------------------+-----------+------------+---------
+
+The material and workmanship of the bridge were good. The rivets of the
+centre girder end diagonals, 1 inch in diameter, were originally 7/8
+inch, but on becoming loose were cut out, the holes reamered, and
+replaced by the larger size, which remained tight, and to which the
+stress figures apply. The rivets in the diagonals near the centre, 7/8
+inch in diameter, which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The riveting in the
+outer girder diagonals, subject to smaller stresses, much more
+frequently developed, also gave trouble, particularly those liable to
+counter stresses.
+
+Apart from looseness of rivets, the general appearance and behaviour of
+the bridge, which had been in existence about twenty years, was not
+suggestive of any weakness.
+
+Of smaller girders, an example showing the necessity for care in
+discriminating, if it be possible, between looseness of rivets resulting
+from over-stress and that due to other influences may first be quoted.
+Two trough girders, of 11 feet effective span, each of the section shown
+in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle,
+with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch
+pitch, showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (Fig. 31). From the nature of the
+arrangement the lower web rivets, which were loose, would receive the
+first shock of the load coming upon the span, but there were evidences
+indicative of original bad work. The angle bars gaped, suggesting that
+these had first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets failing to
+pull the work close, and then readily working loose. Here there is
+considerable uncertainty as to how much of the loosening is to be
+attributed to bad work, and how much to stress. It may, however, be
+remarked that whatever bearing stress was the ultimate result of the
+load hammering on the lower angle flanges, loosening rivets never
+perhaps really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable
+impactive force, was not sufficient to loosen these. The girders were
+taken out after being in place sixteen years.
+
+[Illustration: FIG. 32.]
+
+[Illustration: FIG. 30.]
+
+[Illustration: FIG. 31.]
+
+An instance of undoubted excessive bearing pressure was found in the
+cross-girders of a bridge, mentioned on p. 15, of which so many web
+plates were cracked. This bridge, carrying two lines of way, had outer
+main girders, and long cross-girders with 1/4-inch webs and 3/4-inch
+rivets, 4 inches pitch. The rivet stresses work out at 4�3 tons per
+square inch on each shear surface, and 24 tons per square inch bearing
+pressure. For one road only being loaded, the latter figure falls to
+18�5 tons. The traffic over this bridge, twenty years old, was
+considerable, rapid, and heavy. It is hardly necessary to add that a
+large number of the rivets were loose, one of which is shown in Fig. 32.
+
+[Illustration: FIG. 33.]
+
+To take another case relating to a floor system of extremely bad design
+(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor
+having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches
+deep, supporting hog-backed trough longitudinals. The cross-girders were
+at their ends but 6-3/4 inches deep, the distance from the bearing of
+cross-girders to centre of longitudinals carrying a rail being 2 feet 10
+inches, in which length were eight rivets in the web and angles at the
+top, and six at the bottom, all 3/4 inch in diameter.
+
+The shear stress on the upper rivets works out at 7�3 tons per square
+inch on each shear surface, the bearing pressure 20�6 tons per square
+inch. On the lower rivets the shear stress becomes 9�7 tons, and the
+bearing pressure 27�4 tons, per square inch. Care was exercised in
+computing these stresses, that part of the bending moment carried by the
+web being allowed for, but it must be admitted that the result is,
+probably, approximate only. The sketch here given shows the cross-girder
+end and section. The rivets, though in double shear, were, as might be
+expected, loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled after twelve
+years' use.
+
+In illustration of the behaviour of rivets in the ends of long
+cross-girders, both shallow and weak, and many years in use under heavy
+traffic, may be cited connections having end angle bars to the
+cross-girders, with six rivets through the web of main girders. The
+bearing pressure worked out at 7�8 tons per square inch. Many rivets
+were loose, but it should be remarked that the workmanship was not of
+the best class, and the cross girders flexible: a characteristic very
+trying to end rivets, and inducing a stretch in some, already referred
+to as a possible cause of loosening. This will be apparent if the
+probable end slope of weak girders be considered. The author concludes
+that this inclination should not, for ordinary cases, exceed 1 in 250;
+but the ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly regarded as bad
+practice to submit rivets to tension, yet this is frequently, though
+unintentionally, permitted in end attachments, without any attempt to
+limit the amount of tension. With suitable restrictions, there appears
+no serious objection to rivet tension for many situations.
+
+Another instance of cross-girder end connections of a different type is
+illustrated in Fig. 34.
+
+The main girders of the bridge were 12 feet apart, each cross-girder end
+carrying its share of the half of one road. The mean bearing pressure
+upon the rivet shanks works out at 5�8 tons per square inch for the six
+rivets of the original joint, but in the particular joint shown some of
+the rivets had loosened, making the bearing pressure upon the remainder
+about 8�7 tons per square inch. It is apparent there must have been
+considerable stress on the top and bottom rivets which loosened. These
+two rivets would also, because of difficult access, be in all likelihood
+insufficiently hammered up. The joints worked rather badly; the loose
+rivets had "cut" to a considerable extent, a process materially assisted
+by the gritty nature of the ballast (limestone), particles of which,
+getting into the joint, contributed to the sawing action; this had
+clearly been taking effect for some considerable time. (See Fig. 35.)
+
+[Illustration: FIG. 34.]
+
+[Illustration: FIG. 35.]
+
+The two cases of cross-girder ends given are both rather exceptional in
+character, and in each case the defects appear to be due to general bad
+design and workmanship rather than to any serious excess of bearing
+pressure. This may be illustrated by taking the common case of
+cross-girders, 2 feet deep, carrying two roads, and having end angle
+irons riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which is, for old
+work, simply typical, and does not relate to any specific instance, the
+bearing pressure on the rivets will work out at from 6 to 8 tons per
+square inch, and will seldom be accompanied by looseness of rivets, and
+then only as a result of faulty work.
+
+Some sketches of rivets taken from old bridges have already been given
+in connection with the cases to which they belong; a few others are here
+shown (Figs. 36 to 40) to further illustrate what may be the actual
+condition of rivets after some years' use, and how different from the
+ideal rivet upon which calculations are based. These are, however, bad
+instances.
+
+[Illustration: FIG. 36.]
+
+[Illustration: FIG. 37.]
+
+[Illustration: FIG. 38.]
+
+[Illustration: FIG. 39.]
+
+[Illustration: FIG. 40.]
+
+It should be noticed that rivets may, if in double shear, be loose in
+the middle thickness, due to enlargement of the hole in the central part
+and compression of the rivet, and yet show no sign of this by testing
+with the hammer. There is, however, generally marked evidence of another
+kind in the "working" of the inner part, as, for instance, the web of a
+plate girder, in which case a discoloration due to rust is to be found
+along the edges of the angle bars, or a movement may be detected on the
+passage of live load. Red rust is, in fact, frequently an indication of
+something wrong, when no other evidence is apparent. In plate girders
+having [T] or [L] bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching these
+bars to the cross-girder tops loose, due to causes already dealt with.
+The riveted connection should, as to strength, bear some relation to the
+strength and stiffness of the parts secured, if the rivets are to remain
+sound.
+
+It may be well to give here a summarised statement of the results
+already named, for purposes of ready reference. These by themselves are
+not sufficient to enable working stresses to be deduced, though they are
+instructive. The author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which the rivets
+behaved well, but is not now able to give precise particulars of these.
+
+EXAMPLES OF RIVET STRESSES.
+
+  ---------+-----+---------+------+------+--------+-----------------
+     --    |Span |  Where  |Shear |Single|Bearing | Tight or Loose.
+           | in  |  Found. |Stress|  or  |Pressure|
+           |Feet.|         |  in  |Double|in Tons |
+           |     |         | Tons |Shear.|  per   |
+           |     |         |  per |      | Square |
+           |     |         |Square|      | Inch.  |
+           |     |         |Inch. |      |        |
+  ---------+-----+---------+------+------+--------+-----------------
+  Main    {|  85 |   Web   |  4�0 |   D  |  11�0  | Tight.
+  girders {|  66 |Diagonals|  9�0 |   S  |   9�0  | Many loose.
+          {|  63 |    "    | 14�9 |   S  |  16�3  | Tight generally.
+           |     |         |      |      |        |
+          {|  11 |   Web   |  1�4 |   D  |   7�0  | Tight.
+  Small   {|  26 |    "    |  4�3 |   D  |  24�0  | Many loose.
+  girders {|  11 |    "    |  7�3 |   D  |  20�6  | Loose.
+          {|  11 |    "    |  9�7 |   D  |  27�4  | Loose.
+           |     |         |      |      |        |
+  End     {|  27 |   Ends  |  5�4 |   S  |   7�8  | Loose.
+  connec- {|  12 |    "    |  1�8 |   D  |  {5�8  |}Many loose.
+  tions   {|     |         |      |      |  {8�7  |}
+           |     |         |      |      |        |
+  (Type    |     |         |      |      |        |
+  case)    |  26 |    "    |  4�8 |   S  |   7�0  | Tight.
+  ---------+-----+---------+------+------+--------+-----------------
+
+It is probable that the fact of a rivet being in single or in double
+shear largely affects its ability to resist the effects of bearing
+pressure, as commonly estimated. In the first case, the rivet-shank must
+bear heavily on the half-thickness of the plates or bars through which
+it passes, rather than on the whole thickness; and it is to be supposed
+that under this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.
+
+[Illustration: FIG. 41.]
+
+[Illustration: FIG. 42.]
+
+The author has no very definite information in support of this
+contention, but suggests that for double shear the permissible bearing
+pressure may probably be as much as 50 per cent. greater than for rivets
+in single shear; the difference being made rather in the direction of
+increasing the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this is evident when
+it is considered that the practice has commonly been to make no
+distinction, so that whatever bearing pressures are found to be
+sufficient for both cases may be increased for those capable of taking
+the greater amount. Figs. 41 and 42, here given, illustrate the
+behaviour of rivets under the two conditions.
+
+With reference to the amounts of the stresses to which rivets may be
+subject, the author concludes, as a result of his experience, coupled
+with a consideration of known laboratory tests, that for all dead load
+these may be quite prudently higher than is frequently taken. For iron
+the shear stress to be 10 per cent. less than the stress of parts
+joined; and the bearing pressure--for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary mild
+steel the shear stress to be 20 per cent. less than the stress in parts
+connected, and the bearing pressure equal to it for single-shear rivets;
+and 50 per cent. more for rivets in double shear, though the two latter
+values may probably approach those for wrought iron in steel of the
+higher grades sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction of the
+nominal working stress, arrived at by any one of the methods in use
+which may be adopted, affecting both the parts connected, and the rivets
+connecting them. For reverse stresses it is advisable to keep the shear
+stress in any rivet so low, say 3 tons per square inch, that the
+frictional resistance of the parts gripped by the rivets shall be
+sufficient to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure that,
+if brought to a bearing in one direction by the greater force, it shall
+not go back with reversal of stress. This requirement may be open to
+some question with respect to good machine-riveted work, but for
+hand-riveted connections it may certainly be adopted with wisdom.
+
+The following table will show at a glance how the stresses proposed vary
+with the unit stresses governing the main sections.
+
+PROPOSED TABLE OF RIVET STRESSES.
+
+  -----------+-------------+----------------+----------------
+  Unit Stress|             |Bearing Pressure|Bearing Pressure
+      in     |Shear Stress.|for Single-Shear|for Double-Shear
+    Member.  |             |     Rivets.    |    Rivets.
+  -----------+-------------+----------------+----------------
+              _Wrought Iron.--Tons per Square Inch._
+       3�0   |     2�7     |       3�6      |       5�4
+       4�0   |     3�6     |       4�8      |       7�2
+       5�0   |     4�5     |       6�0      |       9�0
+       6�0   |     5�4     |       7�2      |      10�8
+       7�0   |     6�3     |       8�4      |      12�6
+                 _Steel.--Tons per Square Inch._
+       4�0   |     3�2     |       4�0      |       6�0
+       5�0   |     4�0     |       5�0      |       7�5
+       6�0   |     4�8     |       6�0      |       9�0
+       7�0   |     5�6     |       7�0      |      10�5
+       8�0   |     6�4     |       8�0      |      12�0
+       9�0   |     7�2     |       9�0      |      13�5
+  -----------+-------------+----------------+----------------
+
+  NOTE.--Tension on rivets to be limited to one-half the permissible
+  shear stress, the holes being slightly countersunk under snap-head.
+
+It may be objected that the shear stresses in the proposed table are
+somewhat high for wrought iron and steel. This feature is intentional,
+and is supported by the consideration that whereas there may be loss of
+strength in the members of a structure by waste, there is no such loss
+in rivets, if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective field rivets
+is left to be dealt with as may be considered advisable for each
+particular case, the table as it stands being applicable only to
+riveting not below the standard of first-rate hand work.
+
+Cases of loose rivets in main girders over 50 feet span, due to any
+cause but bad work, are extremely rare, unless resulting from the action
+of some other part of the structure. It may be stated broadly that for
+railway bridges of less than perfect design, the nearer the rail, the
+more loose rivets, generally at connections. This is, no doubt, largely
+due to the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead load, and
+because this effect has been but little modified by the elasticity of
+any considerable length of intervening girder-work. In addition to this,
+it is quite usual to find the rivets more heavily stressed, even though
+the load be considered as "static," in the floor system than in the
+main-girders, though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting--viz., the
+connections--are commonly dealt with by hand; and for this reason it is
+the more necessary to design these with the greatest care.
+
+Any arrangement which favours the gradual acceptance of stress by one
+part from another will contribute to the integrity of riveted
+connections, and lessen the liability of the material to develop faults.
+In other branches of design this is well recognised, but appears in much
+old bridge work to have been entirely overlooked.
+
+Bridges carrying public roads very seldom furnish examples of loose
+rivets; the conditions are generally much more favourable, impact being
+practically absent, full loading infrequent, and the proportion of dead
+load to live, high.
+
+It is, perhaps, hardly necessary to insist upon rivets being, apart from
+mere considerations of strength, sufficiently near together to insure
+close work and exclude moisture. Outside edge seams should never be more
+widely spaced than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections, the
+greater stiffness of the section makes wider spacing allowable up to,
+say, 20 times the thickness; but this must be governed largely by the
+amount of riveting required to pull the parts close together. Where more
+than four thicknesses are to be gripped by the rivets, 3/4 inch in
+diameter is hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed 5/8 inch thick.
+
+
+
+
+CHAPTER VI.
+
+HIGH STRESS.
+
+
+High stress, provided it be well below that at which immediate injury
+results, or possible failure, is not uniformly objectionable. It may be
+first considered relative to the absolute and elastic limits of
+strength, next with respect to the range of stress, and, finally, with
+regard to the frequency of application. For practical purposes--that is,
+for the continued efficiency of a structure--the limit of elasticity
+must be considered to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long as it
+lasts, be liable to the original measure of stress. There may be places
+in a bridge, however, over-stressed only in the earlier period of its
+existence, which, by being over-stressed and suffering deformation,
+permit the origin of this distortion to be harmlessly met in some other
+way. In such a case the injury done to that part does not, of necessity,
+lead to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail after
+being in use but a short time. As for riveting, so in dealing with the
+amount of stress to which a member is supposed to be liable, it should
+be clearly understood by what method this has been arrived at, whether
+the value assigned is the actual measure of the stress, or simply the
+conventional amount arrived at in the conventional way; perhaps
+neglecting web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal amount of
+stress, or including only a partial recognition of those influences. In
+any case quoted the stress named is that at which the author arrives by
+the ordinary methods of computation carefully applied, where these
+appear to be sufficiently precise, unless any qualifying remark be
+added. Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that basis, and
+deducing the stress at the holes from the ratio of net to gross section
+at the extreme fibres; a method more correct than by reference to the
+moment of inertia of the net section. Any exhaustive refinement in the
+study of stresses is not attempted, both because it is beyond the
+author's powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation in
+practice. Effective spans are taken at moderate values, and all
+exaggeration is avoided.
+
+The effects of impact in any part vary so much with nearness to, or
+remoteness from, the living load, and the frequency of development of
+the maximum stress from all causes acting together is so much affected
+by the same consideration, that it is apparent a nominal stress which
+may be harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as ordinarily
+stated--i.e., at so much per square inch, uniform across a section--is
+seldom a cause of trouble. In nearly all cases of failure there is an
+accompanying localised destructive stress, either in rivets or
+elsewhere, with crippling or deformation of some essential part. In the
+tension flanges of main girders with uncomplicated stress, this may run
+up to an amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the compression
+flanges, if these be in themselves sufficiently stiff, or properly
+restrained from side flexure. In support of the above statement may be
+quoted the following instances relating to wrought-iron structures:--
+
+A bridge of 60 feet effective span, having girders immediately under the
+rails, had a flange stress of 6�3 tons per square inch. Another of 64
+feet span, carrying two lines of way, with outside main girders and
+cross-girders, had the flanges of the former stressed to 6�8 tons per
+square inch. A third, of 76 feet span, of similar construction to the
+last, was stressed in the main girder flanges to 7�5 tons per square
+inch. The webs were not included in the computation; the figures,
+therefore, compare with ordinary practice. In these three cases the main
+girders showed no signs of distress, referable to the results stated,
+though the top flanges in the last case were curved inwards. The effect
+of this flexing of the flange would be, of course, to increase the
+amount of compressive stress along one edge, though to what degree
+cannot now be stated.
+
+[Illustration: FIG. 43.]
+
+[Illustration: FIG. 45.]
+
+[Illustration: FIG. 44.]
+
+A further instance of considerable flange stress occurred in a bridge of
+seven nearly equal continuous spans, 25 feet generally, the end and
+greatest span being 29 feet 6 inches, centre to centre of bearings. Some
+details of the bridge are given in Figs. 43 to 45. The four inner main
+girders under rails were 2 feet deep, with webs 1/2 inch thick over
+piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3
+inches by 3 inches by 5/8 inch. There were also two outer girders of the
+same depth, with single [L] bars. Plate diaphragms of full girder depth
+and particularly stiff were carried right across the bridge at the
+centre of the spans, and over the piers. The girders, though evidently
+designed to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see Fig. 45). It is
+doubtful if the girders acted with strict continuity for long after
+erection, as the excessive stress in the rivets of the flange joint
+would, for that condition, have been nearly sufficient to shear them. It
+is probable that this being so, the joints first yielded, relieving the
+bending moment over the piers, and increasing it near mid-span. Whether
+the end spans be considered as strictly continuous with the rest, or as
+simple beams, the maximum bending moments would not greatly differ,
+though occurring for continuity over the pier, for free beams at the
+centre. There is, however, an intermediate condition which makes the
+moments at these two places less than either maximum, but equal to each
+other; a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been calculated,
+giving the minimum stress value that can be accepted. The diaphragm has
+been assumed to transfer to the outer girders a due proportion of the
+load. With this explanation it may now be stated that, under engine
+loads corresponding to those running, the flange stress worked out at
+7�4 tons per square inch tension, web included, or 9�7 tons per square
+inch without considering the web; which stresses, it is more than
+probable, may have been greater. The figures include the consideration
+of anything which may contribute to lowering the stress, and are hardly
+to be compared with those worked to in ordinary design of new work, in
+which it would be quite usual to neglect the assistance of the outer
+girders and the webs, to work to heaviest engine-loads, and possibly
+include an allowance for the effects of settlement. Dealt with in this
+way the girders would seem to be of about one-fourth the strength that
+would be required in the design of a new bridge, in which certain
+elements of strength would be deliberately ignored.
+
+The ironwork was in good condition, there was no ordinary evidence of
+weakness apart from the calculated results, the vibration was distinctly
+moderate, and the deflection, though not recorded, was certainly small.
+The bridge did, indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long overstressed
+may have a sensibly higher modulus of elasticity than newer work at more
+moderate stresses. The traffic was not very considerable, and both
+roads, of the same spans, but seldom loaded at the same time; though
+with this construction of bridge there would in either case be very
+little difference. The author recalls no reason for supposing that the
+piers had yielded in any sensible degree. The bridge was rebuilt after
+some thirty-six years' use.
+
+Stress of considerable amount in the flanges of a latticed main girder
+of 63 feet span has already been noticed in the chapter on "Riveted
+Connections," which for the tension boom worked out to 7�1 tons per
+square inch, the flanges in this case showing no signs of weakness. An
+instance has also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons per square
+inch, the girder recovering its form when relieved of load.
+
+As to stress in cross-girder flanges, an example may be quoted of a
+bridge of 109 feet span, carrying two roads, having outside main
+girders, with cross-girders between; these latter were stressed in the
+flanges to 6�7 tons per square inch (webs not included), if the partial
+distribution among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some reason to
+think in this instance that distribution had the effect of reducing the
+stress quoted, as the observed deflection of the cross-girders was
+materially less than that calculated for girders acting independently of
+each other, though this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the heavy main
+girders, would also tend to moderate the stress. No very definite
+conclusion can therefore be deduced from this instance.
+
+To take another case of less uncertainty, the bridge of 35 feet span
+(see Fig. 33), referred to in "Riveted Connections," may again be cited.
+The extreme fibre stress in the cross-girder flanges worked out at 6�3
+tons per square inch, web included, or 6�5 tons, exclusive of the web.
+It cannot be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was 1/2 inch on the span of
+11 feet, in addition to a permanent set of 3/4 inch, largely due,
+however, to "working" rivets.
+
+A better and altogether conclusive case of the way in which
+cross-girders may occasionally suffer considerable stress, and show no
+sign, is furnished by two cross-girders, of which some particulars are
+here given. These girders occurred in the floor of a very acute angled
+skew bridge, riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end on a masonry
+abutment. The first girder was about 19 feet effective span, 12 inches
+deep in the web, with angle bar and plate flanges. The girders were
+spaced 6 feet apart, and were connected under the rails by [T]-bars,
+cranked down to face the webs, and riveted through. Though these [T]'s
+had little stiffness, yet the frequent vertical movements of the girders
+relative to each other, under passing loads, had broken the majority of
+the [T]-bars at the bends, so that no notice need be taken of these as
+transferring load from any one cross-girder to its neighbour. The floor
+covering consisted of timbers about 4 inches thick, also incompetent to
+transfer any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers, chairs,
+and ordinary bull-headed rails. The stress to which the girder was
+liable works out at 8�4 tons per square inch, on the extreme fibres of
+the net section, web included; or 9�1 tons, neglecting the web, under
+engine-loads of a common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with angle bar
+and plate flanges. The stress per square inch was 10�5 tons, web
+included, or 11�1 tons per square inch, neglecting the web. This girder
+carried three rails, one of which was near to the abutment bearing, so
+that there was no great difference in the stress induced whether all
+three rails were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a common
+occurrence for the girders to take the full loads. The heavier engines
+passed scores of times in a day--lighter engines probably one hundred
+times. The bridge was about twenty years old, yet these cross-girders,
+when removed, showed no other sign of age and wear than that due to
+rust.
+
+[Illustration: FIG. 46.]
+
+All the foregoing instances relate to wrought-iron bridges. Two cases of
+steel construction are here added, the first of these furnishing an
+example of high girder stress somewhat remarkable. This was found in a
+trough girder of a strange pattern, of which a section is here given
+(Fig. 46). The bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a crawling
+pace. The larger of the two girders carrying the rails was 15 feet 8
+inches effective span. The sides of the trough consisted each of two
+vertical plates, originally 1/2 inch thick, but wasted to an aggregate
+thickness of 5/8 inch. These plates 6 inches deep, were connected at
+their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which
+again were riveted to a bottom plate 16 inches wide, originally 1/2 inch
+thick, wasted to 3/8 inch. Lying in the bottom of the trough, and
+riveted through the inner angle flanges, was a bridge-rail. Assuming
+that the metal retained its elastic properties from top to bottom of the
+section, at whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the net section.
+As puddled steel, of which the girders were made, may have a tenacity of
+45 to 55 tons per square inch, the assumption is probably correct. The
+author has no record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine passing over,
+required some determination.
+
+A point of additional interest in this little bridge is that, though
+made of steel, it dates as far back as 1861, having been in use
+thirty-two years when removed. The particular variety of steel used was
+known as Firth's puddled. The evidence of this consists in
+correspondence showing that permission had been asked of the controlling
+authority, by the only users of the siding, to apply this material, with
+no evidence of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some girders of
+considerable span. The appearance of the trough girders to which the
+foregoing particulars apply was distinctly different to that which might
+be expected in ordinary wrought iron. The top edges of the vertical
+plates were wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which the girders
+held up to their work for so long is, by itself, conclusive on the
+point. The bridge-rail appeared to be of wrought iron, the different
+modulus of elasticity of which has been included in the calculation upon
+which the preceding results are based. That these girders stood so well
+is, perhaps, largely due to the fact that the load carried by them was,
+though varying within wide limits, practically free from impact, which,
+had the load passed over quickly, would, with girders so small, shallow
+and flexible, have been very sensible.
+
+The second instance of steel construction in which somewhat high stress
+is manifest is that of some steel troughing of the Lindsay pattern, used
+in a bridge built in 1885. The troughs ran parallel to the rails, having
+an effective span of 18 feet 8 inches. The depth of the section (which
+is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span
+of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.
+
+[Illustration: FIG. 47.]
+
+Assuming this to be carried on six troughs, which corresponds to 11 feet
+3 inches of width, the extreme fibre stress works out at 7�5 tons per
+square inch, under usual engine-loads. The bridge when examined after
+fourteen years' use was in good condition, and at that time but little
+rusted; but the end seam rivets were, as is not uncommon with such
+troughing, loose. The traffic over the bridge was considerable, but not
+at great speed.
+
+On the opposite page are set out the results which have been given, in
+tabulated form, as was done for rivet stresses, to enable ready
+comparison to be made.
+
+EXAMPLES OF HIGH STRESS.
+
+  --------------+-----+---------+---------------+--------+-----------
+                |Span |  Part   |  Stress per   |Tension |Condition.
+                | in  |Stressed.|  Square Inch. |   or   |
+                |Feet.|         +-------+-------+Compres-|
+       --       |     |         | Webs  | Webs  | sion.  |
+                |     |         |  In-  |  not  |        |
+                |     |         |cluded.|  In-  |        |
+                |     |         |       |cluded.|        |
+  --------------+-----+---------+-------+-------+--------+-----------
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |60�0 |Flange   |   ..  |  6�3  |Tension | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |64�0 |   "     |   ..  |  6�8  |   "    | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |76�0 |   "     |   ..  |  7�5  |   "    | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |    {|   "     |  7�4  |  9�7  |   "    |}
+  main girders, |29�5{|   "     |  6�3  |  8�3} |Compres-|}Good.
+  plate         |    {|         |       |     } |sion    |}
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |63�0 |   "     |      7�1      |Tension | Fair.
+  lattice       |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |47�0 |Flange   | 10�0  |   ..  |Compres-| Fair.
+  plate         |     |edge     |       |       |sion    |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|26�0 |Flange   |   ..  |  6�7  |Tension | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|11.0 |   "     |  6�3  |  6�5  |   "    | Bad; loose
+  plate         |     |         |       |       |        | rivets.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|19�0 |   "     |  8�4  |  9�1  |   "    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|22�0 |   "     | 10�5  | 11�1  |   "    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Steel trough  |    {|   "     |     15�0      |   "    |}Fair,
+  girder        |15.7{|Top edge |     32�0      |Compres-|}but
+                |    {|         |       |       |sion    |}rusted.
+                |     |         |       |       |        |
+  Steel         |18�7 |Flanges  |  7�5  |   ..  |Tension | Fair,
+  troughing     |     |         |       |       |and Com-| but
+                |     |         |       |       |pression| rusted.
+  --------------+-----+---------+-------+-------+--------+-----------
+
+It would be unwise to infer from the instances which have been quoted
+that high stress may be regarded with complaisance. In the most
+conscientious engineering work there should still be a liberal margin
+for material possibly defective, or even bad, for waste and
+deterioration, and for the aggregate effect of minor errors in design,
+any one of which considerations, except the first, by itself might not
+be of great importance. The conclusion which may, however, be derived
+from this and the previous chapters is, that bridge failures are less
+likely to occur from high stress of a kind readily calculated than from
+failure in detail, obscure and little suspected, the reason for which is
+not perhaps apparent, till the attention is forcibly directed to it by
+the refusal of the structure to sustain the forces to which it may be
+liable.
+
+
+
+
+CHAPTER VII.
+
+DEFORMATIONS.
+
+
+Instructive lessons are to be had from a study of the various
+alterations in form to which metallic bridgework is liable, which
+alterations may be due simply to the development of stress of ordinary
+amount, and are then generally small; or to abnormal stresses, the
+result of some distortion in the bridge structure itself not originally
+intended, and possibly extreme. In addition to these there may be
+deformations due to settlement, to "creeping" of parts of the structure
+relative to the rest, to temperature changes, to rust, and to original
+bad workmanship. In any instance quoted below the methods adopted to
+ascertain the amounts of such alterations were quite simple, even crude;
+but as care was exercised, and no attempt made to measure any very
+minute changes, the results may be accepted as practically correct.
+
+Dismissing for the present changes of form such as are to be expected,
+and touched upon in other places in this work, with respect to the
+particular parts of bridge structures affected by them, a few instances
+will be adduced of alterations which, though not very surprising, are
+such as in the design of the work are hardly likely, in most instances,
+to have been contemplated.
+
+A case has already been referred to in which, owing to eccentric loading
+of main girders, these were, as to the top flanges, flexed sideways a
+considerable amount. It is proposed to supplement this by further
+remarks relative to somewhat similar cases. A like effect is frequently
+to be observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting ledges
+formed by the bottom angle-bars of such troughs. In old forms of this
+arrangement it is common to find the two girders forming the trough
+connected only by bolts passing through the timbers, or just above them
+and below the rails; or connected by narrow strips, which serve no other
+purpose than to prevent the sides spreading at the bottom. The top
+flanges in such cases commonly curve inwards on the passage of the
+running load, accompanied of necessity by an increase of compressive
+stress upon the outer edges of the flanges, and perhaps by the working
+of any flange-joint which may exist. This, both as to flexing of the top
+flange and the working of a joint, was noticed in the case of a bridge
+twenty-three years old, very similar to that illustrated in Figs. 8 and
+9, and described on pages 13 and 14. The top flange consisted, however,
+of a bridge rail riveted to the top edge of the web, butting at a joint,
+and covered by thick cover strips (see Fig. 48). The joint itself was
+poor, and depended largely upon the character of the butt, which was not
+sufficiently good to prevent the top member kinking at this point, under
+the joint influence of transverse effort and compressive stress, with
+possibly some help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked in passing that it is
+very objectionable to use bolts as was done in this instance; for as the
+timber settles down on its seat, taking the bolts with it, these bear
+hard in the webs, enlarging or even, as in this case, tearing the holes,
+accompanied by injury to the bolts themselves. The practice is now
+almost obsolete, but the example is instructive as showing the
+impropriety of securing timbers by bolts passing through them at right
+angles to the action of the load, unless these bolts are quite free to
+move with the timber as it compresses.
+
+If trough girders must be used, the better plan is to connect the two
+sides by a continuous bottom plate, the trough thus formed being
+properly drained, if the timber is not bedded in asphalt concrete; or to
+introduce stiff diaphragms at intervals beneath timbers, if the depth
+suffices.
+
+In the case just quoted the curvature of the top members of the girders
+was inwards, but in the instance given below, of twin girders 26 feet
+effective span, with longitudinal timbers between, resting, as before,
+upon the inner ledge formed by the bottom flanges, the curvature was
+observed in three out of four girders to be 1/2 inch in a contrary
+direction, the fourth remaining straight.
+
+[Illustration: FIG. 48.]
+
+[Illustration: FIG. 49.]
+
+An inspection of the accompanying section, Fig. 49, will, perhaps,
+render the reason evident when it is noticed that the top members are
+very unsymmetrical in form, the effect of this being to give these
+members, under stress, a strong tendency to flex outwards, apparently
+more than sufficient to counteract the tendency of an eccentric
+application of load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be not
+materially in excess, and is actually so, only because the thinness of
+the web--1/4 inch--renders it incompetent to keep the bottom flange up
+to its work, and so secure the full effect of the eccentric loading in
+limiting the outward tendency, due to the section of the top member,
+the effects of which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange to the other
+prevent the want of symmetry noticed in these--which, by the way, is on
+the wrong side for utility--from having any particular effect.
+
+To give one other example of the consequences of eccentric loading, a
+bridge of 48 feet effective span may be quoted. This bridge carried four
+lines of way supported by five main girders, trussed by kicking-struts
+in such a manner as to form a bastard arch. A part section and plan are
+given in Figs. 50 and 51.
+
+[Illustration: FIG. 50.]
+
+[Illustration: FIG. 51.]
+
+The floor consisted of Lindsay's troughing resting upon the lower
+flanges of the main girders, the three middle girders, subject to
+eccentric loading, sometimes on one side, sometimes on the other, were,
+with dead load only, straight; but the two outer girders, liable to
+loading only on one side, had, under repeated applications of such a
+load, assumed a permanent curve towards the rails--13/16 inch in one
+case and 1 inch in the other--which curvature, no doubt, increased when
+a live load came upon the contiguous roads, though this was not
+measured. It should be remarked in passing that, owing to settlement and
+the canting of the abutments, the three middle girders were also
+"down"--in one case 3/4 inch. The girders, with one near road loaded,
+deflected 1/8 inch--greatly less than would have been the case had the
+main girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.
+
+Deformations due to settlement may be very considerable. The author
+recalls two instances affecting continuous girders. In the first of
+these, a bridge twenty years old, of two spans of about 50 feet each,
+and with girders 4 feet 6 inches deep, the centre pier had sunk 4
+inches, reducing the spans, as respects the dead load, practically to
+the condition of simple beams, just resting, but hardly bearing, upon
+the piers when free of live load.
+
+In the second case, also of two openings of about 55 feet each, with
+girders 8 feet deep, one abutment had sunk about 3 inches, more than
+doubling the stresses over the centre pier. It is manifest that
+continuous girders should only be adopted where settlement of the
+supporting points is not likely to occur to any material degree. If this
+cannot be relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to make a liberal
+allowance for settlement stresses, in which case any economical
+advantage that should exist will probably disappear. It is, however, to
+be acknowledged that so long as the girders are in touch, under dead
+load, with the bearings intended to support them, the stresses due to a
+live load are unaltered, the principal effect in this case being that
+the variation in stress due to the live load ranges between limits that
+are higher or lower in the scale of stress than is the case with
+bearings undisturbed; still, if it is desired that the maximum stress
+shall not exceed, say, 6 tons per square inch, it can hardly be a matter
+of indifference that settlement shall induce a maximum of, perhaps, 10
+tons, as in that case the stress must be 4 tons nearer the limit of
+statical strength.
+
+Before leaving this matter it may be well to point out that in the case
+of continuous girders of uniform section a moderate settlement of the
+piers may even be advantageous by reducing the moments over the piers,
+and possibly making them equal to those obtaining near the middle of the
+spans, in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.
+
+Bridges consisting of simple main girders connected by cross-girders may
+be very prejudicially affected by unequal settlement; for instance, if
+one girder bearing settles more than the others, a twist is put upon the
+structure very trying to the floor-girder connections, and possibly to
+the main girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments. Indeed,
+settlement of this kind may be much more destructive to a metallic
+bridge than to an arch of brick or masonry, the commonly accepted
+opinion notwithstanding.
+
+Instances of deformations due to the creeping of some part of the
+structure away from its work, are within the author's knowledge, rare;
+except in the case of the ends of main girders in skew bridges, already
+referred to.
+
+Distortion, the result of temperature changes, is frequently to be
+observed in any considerable length of girder flange or parapet where
+there is not freedom of movement, unless due provision is made to check
+it.
+
+It is quite common to see parapets out of line, either because the ends
+are not free, or because the light work of the parapet being more
+exposed to the sun's rays than the girder work to which the lower part
+is attached, expanding to a greater degree, is subject to considerable
+compressive force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or flexible
+joints at moderate distances apart, or to make the parapet sufficiently
+stiff to take the stresses developed, without crippling. A parapet may
+also go out of shape if directly attached to the top flange of a girder
+liable to heavy loading, particularly if the girder be shallower than
+the parapet, simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the girder
+proper.
+
+Rivets spaced too far apart, by allowing the plates or other parts to
+spring open slightly, and permitting moisture to enter, results in the
+growth of rust, which, as it swells in forming, forces the parts
+asunder, and may set up considerable stress.
+
+Flat bars riveted together by rivets spaced 12 inches apart may from
+this cause be forced asunder, as much as 1/2 inch, sufficient to set up
+a stress, with any practicable thickness of bar, much exceeding the
+elastic limit.
+
+Local distortions may occur as the result of imperfect workmanship or
+careless erection, causing quite possibly very severe local stresses; or
+girder flanges may be out of straight as a result of riveting up along
+one side first, instead of advancing the riveting simultaneously along
+the whole breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is sometimes
+done to girderwork during manufacture by rough treatment to make the
+work come together; but the author has little to offer with respect to
+these matters that is not common knowledge. It may, however, be pointed
+out in passing that a bridge upon the design of which great care has
+been expended, with the idea that theoretical propriety shall not be
+violated, may be completely spoiled in this respect by careless
+construction. Fortunately, both steel and wrought iron, if of good
+quality, are long suffering. Incompetent erection will sometimes result
+in the true girder camber not appearing, or in differences as between
+girders supposed to be similar. This is not, of course, a deformation in
+the sense in which the word has previously been used, but it is
+desirable to bear the fact in mind as a possible cause of defective
+camber in dealing with questions of deformation.
+
+The foregoing has reference chiefly to alterations of form in bridgework
+of wrought iron or steel, but a case of considerable interest is that of
+a cast-iron arched structure, of which the author made a very complete
+examination.
+
+[Illustration: FIG. 52.]
+
+[Illustration: FIG. 53.]
+
+This bridge, built in 1839, and carrying two lines of railway, consisted
+of three spans, 100 feet each, of 10 feet rise, made up of four inner
+and two outer ribs, each rib being in three nearly equal parts; the
+floor was of timber, the abutments and piers of masonry. As originally
+constructed there was no bracing between the ribs other than the frames
+indicated on the plan here given (Fig. 52), stretching from outer rib
+to outer rib in the neighbourhood of the rib joints, which were simple
+butts without bolts or any equivalent means of connection. The floor
+was, however, braced in the horizontal plane, and the structure was also
+braced over the masonry piers. After forty-two years' use supplementary
+distance-pieces were introduced between the ribs, but still no bracing
+between them, or any efficient means of checking lateral movement. A
+crack developing in one of the outer ribs at the crown, led to an
+investigation to trace the cause, the bridge then being fifty-four years
+old. Careful plumbing of the abutments revealed the fact that three out
+of four abutment pilasters were out of the vertical, as shown in Figs.
+52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner
+from which the cracked rib had its springing; there was also other
+evidence of settlement in an old crack extending from the top of the
+abutment to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were also out of
+plumb, that which was cracked being 2-1/2 inches out at the centre. The
+joints of the ribs, which, as already stated, were simple butts, in some
+cases opened and shut, as the load passed over, in such a way as to
+suggest that the ribs were acting, in a manner, as four-hinged arches,
+of which two hinges were at the springing, and the other two at the
+joints, one of which would for most positions of the load be out of use,
+reducing the rib to the three-hinged condition; in other words, as the
+rolling load passed over the span, one or other of the two joints of a
+rib would "gape" an appreciable amount at the bottom or at the top.
+Observations were taken by means of a theodolite placed below, either
+upon the bank or upon the tops of the masonry piers, sighting upon
+suitable scales attached to the ribs to ascertain the amounts of
+vertical and horizontal movement during the passage of trains over the
+bridge. The principal results are set forth in the following table:--
+
+MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT.
+SPANS.
+
+  ----------------------+-------+----------+-----------
+                        |Fall in| Rise in  | Lateral
+            --          |Inches.| Inches.  | Movement
+                        |       |          |in Inches.
+  ----------------------+-------+----------+-----------
+                      _Span No. 1._
+  At A. Up road loaded  |  �20  |   �08    |   �04
+   " A. Down road loaded|  �08  |   �03    |   �04
+   " B. Down road loaded|  �14  |No record.|   �02
+                      _Span No. 2._
+  At C. Up road loaded  |  �40  |   �13    |  Slight.
+   " C. Down road loaded|  �10  |   �05    |     "
+                      _Span No. 3._
+  At D. Up road loaded  |  �22  |No record.| No record.
+   " D. Down road loaded|  �15  | Slight.  |  Slight.
+  ----------------------+-------+----------+-----------
+
+  NOTE.--The lateral movements are to either side of the mean position.
+
+The particulars for spans 2 and 3 were obtained with the instrument set
+up on the pier between these spans. The tremor of this pier was such
+that no useful readings for lateral movement could be obtained. Further,
+as the rolling load came upon these spans, the effect was to rock the
+pier to an extent vitiating the readings for vertical displacement; but
+by sighting upon the fixed abutment, and observing the amount of this
+rocking, suitable corrections were made in the apparent rib movements.
+The figures given in the table are thus corrected. The pier rocking was
+equivalent, as an extreme, to an inclination from the vertical of 1 in
+3200. An attempt to measure the horizontal movement of the pier-top was
+unsuccessful, owing to the impracticability of setting up the instrument
+in a suitable position, sufficiently near to the pier to enable readings
+to be satisfactorily taken. This horizontal displacement probably
+amounted to about 1/16 inch either way. The rise and fall of the arches,
+and rocking either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect to the
+spans. Summarising the results, the greatest vertical movements
+downwards were 0�20 inch, 0�40 inch, and 0�22 inch for spans Nos. 1, 2,
+and 3, the upward movements being 0�08 inch and 0�13 inch for the first
+and second spans, there being no recorded result of this kind for the
+third span. With adjacent ribs loaded, the movement of the ribs unloaded
+was one from one-third to one-half of the full amounts. It is to be
+noted that the lateral displacement in no case exceeded 0�04 inch either
+way, nor were the vertical movements exceptional; yet, as a matter of
+sensation, when seated upon the ironwork, it was a little difficult to
+believe them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0�45 inch, 0�45 inch, and 0�55
+inch for the spans in order, the extreme temperatures being fairly
+representative of the English winter and summer. The structure was, as a
+consequence of the examination, efficiently braced by diaphragms between
+the ribs, and diagonals following the arch ribs round from springing to
+springing, with satisfactory results. The crack already referred to, and
+its probable causes, will be dealt with under "Cast-Iron Bridges."
+Eventually this bridge was reconstructed to meet the requirements of
+growing engine-loads.
+
+
+
+
+CHAPTER VIII.
+
+DEFLECTIONS.
+
+
+Deflection, considered only as a fraction of the span, and without
+regard to other conditions affecting it, is of very little use as an
+indication of a girder's fitness for its work; but when taken with
+reference to the depth of the girder, the nature and amount of the load
+producing flexure, and, further, with regard to the quality of the
+workmanship and normal properties of the material of which the beam is
+constructed, it may be of some little service in helping to form a
+reliable opinion. This consideration applies with less force, perhaps,
+to new work than to old, in which there may be unknown influences at
+work, or unknown defects which by excessive deflection may be betrayed.
+Though too much importance should not be attached to results of
+deflection tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each case, gives a
+good general idea of what may be expected in a fresh instance, any
+material departure from which should be a reason for specific inquiry as
+to the cause. A further reason with new work is found in the evidence it
+affords as to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case of floor
+beams, in what way the load is distributed amongst them, if, indeed,
+there be any such distribution.
+
+The author has commonly found that new work gives greater deflections
+than old--i.e., while calculation gives the same result for each, it
+does not apply equally well to both. The differences may be accidental,
+but are probably due to other causes, perhaps to the fact that new work
+has not by repeated applications of load lost the resilience of parts
+liable to considerable local stress, such as is very liable to occur at
+connections, so that the deflection is, whilst new, greater than after
+many years' use, by which time such parts may develop a definite "set,"
+and contribute in a less degree, or not at all, to the total elastic
+deformation.
+
+It is also possible, as already suggested, that repeated high stress may
+reduce the ratio of strain to stress, the material gradually becoming
+more rigid, the modulus of elasticity being, in fact, increased.
+
+In girders of ordinary construction, the major part of the deflection is
+due to the booms, the remainder to the web; the latter is for plate
+girders a small amount only, and is commonly neglected, but for open web
+constructions it may be quite appreciable. For any given type of web
+arrangement the deflection due to the web will, for all depths, remain a
+constant quantity for the same span and unit stress; and though a
+moderate fraction of the whole deflection for a shallow girder, it may
+be a very considerable part for a girder of great depth, in which that
+part due to the booms is, of course, smaller, since the deflection due
+to these varies inversely as the girders' depths.
+
+Deflection, being dependent upon the elasticity of the material, is of
+necessity very largely influenced by the value of its modulus E, itself
+liable to considerable variation, and is increased in a small degree by
+the yield of joints and rivets, which effect, apart from the initial
+"set" of the girders, appears to be negligible. The stiffness of members
+in resisting angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less, and,
+finally, section excess at joints and gusset attachments has an
+influence in modifying deflection as compared with that due to the
+normal gross sections simply.
+
+From these considerations it is apparent that any simple deflection
+formula must be largely empiric in its nature. For plate girders of
+uniform depth and flange stress, the writer has found the following to
+give good results:--
+
+    S�
+  ----- � _f_ = deflection in inches.
+  D � C
+
+The span S and depth D are, as a matter of convenience, taken in feet;
+the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is
+the mean of the extreme tensile and compressive stresses of the booms,
+in tons per square inch, estimated upon the gross sections.
+
+This, though satisfactory for plate girders, is not so suited to girders
+having open webs, in which the deflection will more nearly be
+
+  (3S     S� )
+  (-- + -----) � _f_,
+  (C    D � C)
+
+the constant C being 3900 and 4450 for iron and steel respectively. The
+latter values of C correspond to normal values of the modulus of
+elasticity of 11,700 and 13,350 tons for iron and for steel, it being
+assumed that any slight rivet yield is off-set by any small section
+excess--say, 5 per cent.; it may, however, happen that section excess is
+greater than assumed, in which case some allowance may properly be made
+for this by increasing C.
+
+To adapt the formul� to girders other than those having parallel booms
+and uniform stress, the results, as deduced above, may be multiplied by
+constants given in column B of the Table given on page 93.
+
+The practice of adopting for E in deflection formul� a quantity much
+smaller than its nominal amount, with the object of allowing in riveted
+girder work for the yield of rivets and of joints, can hardly now be
+defended, whatever may have been a case at a time when workmanship was
+much inferior, when there was no machine riveting, and joints were,
+owing to the small weight of plates and bars, three times as numerous.
+
+The initial "set" of a girder consequent upon first loading is a
+quantity quite distinct from deflection proper, and may be so small as
+to be negligible, or read 10 per cent. of the true deflection, varying
+with design and workmanship.
+
+No estimate of girder deflection can be even approximately true if there
+is, at the level of the top or bottom flanges, a plated or otherwise
+rigid floor system which is not taken into account, as this will have
+the effect of very materially reducing the boom stress. To neglect this
+influence, where it exists, must necessarily lead to disappointing
+results, and it is quite practicable in many instances to include it in
+the calculation.
+
+The influence of angular distortion between the various members has been
+neglected. It may be pointed out, however, that the resistance
+accompanying these movements in girders having riveted connections,
+though unimportant as affecting deflection, is worth some consideration
+in regard to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount for any span,
+but will generally be of less importance in large girders than in small,
+because in large girders the ratio of the breadth of members to their
+length is commonly less.
+
+When determining the probable deflection of any girder of exceptional
+figure, it will be found convenient to make a strain diagram--an old
+device, in which the actual alterations of length being ascertained for
+all members, the girder is carefully set out to a suitable scale, with
+the lengths of members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the probable
+deflection. The value of E for this purpose should never be taken at
+less than the normal amount, and may for a considerable excess of metal
+in joints and gussets be made as much as 10 per cent. greater, this
+being a convenient means of making the necessary correction.
+
+The effect of loads quickly applied may here be considered in connection
+with elastic deformations of girders of the same span, but different
+depths. If these be designed for similar loads and unit stresses, the
+deflections due to webs and booms of the girders compared will bear the
+same relation, each to each, as do the weights, whether in both cases
+the loads be inert or quickly applied, from which it follows that the
+mechanical "work" done by the loads in falling through the deflection
+heights is, neglecting inertia, always in proportion to the girderwork
+weights, and is a similar amount per ton, which as the total length of
+members remains substantially unaltered, corresponds to a similar amount
+of work per unit of section, or similar stress, irrespective of the
+depth of the girders.
+
+But for a "drop" load, as when there is some obstruction upon a railway
+bridge, there will be in addition a further amount of work to be
+absorbed, which is to be considered the same whatever the girder's
+depth, and will for deep girders be a larger amount per ton of
+girderwork than in those that are shallow; this, taking effect on
+members of the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in the booms.
+
+The influence of the girder's inertia in modifying drop-load effects
+will also be less marked in deep--i.e., light--girders than in girders
+shallow and heavy.
+
+It is, notwithstanding all this, desirable that the depth of main
+girders should be liberal for economy's sake, and also that of floor
+beams, for reasons already dealt with; the probability of the drop load
+is somewhat remote, and, though possible, would simply induce, if it
+occurred, an increment of stress rather more important in deep girders,
+making it specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact effects.
+
+It should be remarked that for short and very flexible beams, generally
+outside the limits of practice, there may also be, under quickly moving
+loads, a material increase of stress due to the centrifugal effort of
+the load on running round the deflection curve, and in rising upon the
+steep part of the curve beyond the girder's centre. Where advisable,
+these effects may be modified by cambering the rail.
+
+For pin bridges in which there may be spring in the pins, excess stress
+in some eye-bars due to inequalities of length, and a want of that
+rigidity peculiar to riveted structures, the deflection will be greater
+than above indicated for girders of the ordinary English type.
+
+The method in common use for measuring the deflections of girders but a
+moderate distance above the ground by means of sliding-rods, though
+crude, gives, with care, results sufficiently accurate for most
+practical purposes; but some points necessary to remember may be
+mentioned with propriety. The lower rod should rest firmly upon
+something solid, say a stone, well bedded and free from any tendency to
+rock; the upper end should bear against some part of the girder above,
+presenting a hard surface, free from dirt or scale, and as the running
+load approaches the bridge it should be ascertained that there is no
+slack, that the rods bear hard at the top and bottom. The upper end
+having been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other. These
+precautions are so self-evident that an apology is almost necessary for
+mentioning them.
+
+To ascertain deflections with a single pair of rods is only allowable
+when the girders rest firmly on their bearings; if felt has been placed
+under the girder ends, or if the bedstones are insecure or rocking, it
+is necessary to use three pairs of rods, one pair at the middle and a
+pair at each end, in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the desired
+result.
+
+In the case of a number of spans in series, each resting upon sill
+girders common to two sets of bearings, this method also gives results
+of indifferent reliability, as the depression of each end may be greater
+as the travelling load comes upon and leaves the span than when it is
+precisely over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular position of
+the running load, which are what is required.
+
+The author suggests, as a means of ascertaining deflections free from
+these objections, that it should be done by first measuring the slope at
+one end, and from this deducing the deflection at the centre.
+
+This is to be accomplished by means of a little instrument, consisting
+of a telescope with cross-hair sights, and fitted with a reflecting
+prism at the eye-piece capable of being turned round, so that the
+observer has a wide choice as to the position he assumes with reference
+to the instrument, and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one end of the
+girder over the bearing, at the other end a scale is secured, to which
+the telescope is directed, the cross hair being made to sight on the
+zero of the scale, or the reading noted. For a girder supposed to
+deflect to uniform curvature (say, with uniform depth and uniform
+stress, the ordinary case) the reading observed will be four times the
+deflection; every 1/10 inch actual reading on the scale will correspond
+to 1/40 inch of girder deflection.
+
+Apart from the deflection, this method gives a ready means of observing
+the end slope, a quantity of equal value for purposes of comparison. As
+with girders of similar proportions, and similarly stressed, the
+deflection will at all spans be the same fraction of the span; so should
+the end slope be a constant quantity under similar conditions, the
+diagram, Fig. 54, will make the principle quite clear.
+
+[Illustration: FIGS. 54 to 57.]
+
+Strictly the character of the deflection curve is slightly modified by
+that part of the deflection due to the web; so that the depression at
+the centre would, in the case assumed above, be somewhat more than
+one-fourth part of the end reading, and generally will be a larger
+fraction of the reading than that deduced from a consideration of flange
+stress simply. In Figs. 55 to 57, which are intended to explain this,
+it will be noticed that deflection due to the web is shown
+straight-lined from the bearings to the centre of the girder; this is
+strictly true only for a girder correctly designed for an immovable
+distributed load; but as there should be for girders intended for a
+travelling load, some excess in web members near the centre under the
+condition of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as shown in the
+diagram for the sake of simplicity.
+
+Suitable constants, including the corrections necessary, are given in
+column A of the table annexed for a few typical cases, and by these
+constants the actual readings should be multiplied to find the
+deflection. The constants have been worked out for depths of one-tenth
+the span; for greater depths they should be slightly more, and for
+smaller depths somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly exceeding 5
+per cent., and generally much less.
+
+The figures in column B relate to the formul� previously stated, and
+apply equally well to all depths.
+
+TABLES OF MULTIPLIERS FOR DEFLECTION.
+
+  _Uniform Stress_:                                           A.     B.
+      Girders of uniform depth, varying flange section       0�27   1�00
+      Hog-backed girders, ends half of centre depth, varying
+      flange section                                         0�24   1�08
+  _Varying Stress_:
+      [1]Girders of uniform depth and flange section         0�32   0�87
+      [1]Hog-backed girders (as above), but uniform flange
+      section                                                0�29   0�97
+      [1]Bow-string girders of uniform flange section        0�16   1�30
+
+[1] For uniform loading.
+
+It is apparent that, if preferred, the scale, instead of being in
+inches, divided suitably, may, for each type of girder, be amplified to
+the proper degree, so that the amount of the deflection may be read off
+at once.
+
+This method of dealing with deflections is quite independent of the
+character of the bearings, and is applicable to girders at any height
+above ground or over water; but its use would hardly be practicable for
+very small beams, or those in an awkward position, or near which it
+would be impossible to remain with a running load upon the bridge.
+
+There is a possible source of error in the use of the instrument, most
+likely to occur with triangulated girders, with which, if the instrument
+is placed at the top of an end post, the reading observed may be the
+joint effect of deflection and of local flexure of the members meeting
+near the telescope. This may be tested, and, if necessary, allowed for,
+by first sighting upon a scale at the next apex, and observing the
+effect of the moving load. Again, as girders sometimes cant towards the
+running load, if the instrument is placed on one edge of a girder, and
+the cantings of the two ends are dissimilar, a false reading will
+result, which may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between the cants
+upon the observation. Only in exceptional cases is it likely that either
+of these considerations would need attention.
+
+The author has secured with this instrument very promising results,
+notwithstanding that under a running load there is a slight haziness of
+the scale as seen through the telescope, due to "dither," largely the
+result of imperfections which may be remedied.
+
+Deflections may sometimes be conveniently taken, by a quick-eyed
+observer, with a good surveyor's level and a specially-divided staff
+held at the centre of the girder. The divisions preferred by the author
+for this purpose are 1/10 inch, plainly marked, which may be seen at 50
+feet distance with sufficient clearness to make possible readings by
+estimation between the divisions to, say, 1/50 inch. But it is clearly
+desirable not to rely upon a single observation only, where all the
+evidence is gone so soon as the sight has been taken.
+
+In rail-bearers, or other short girders, it may not be practicable to
+adopt such methods, either on account of an inability to find a suitable
+place for the instrument, or to read with any telescope with sufficient
+promptitude as the load passes rapidly over. The use of rods may also be
+out of the question, as the errors attending their manipulation may be
+serious where but a small movement has to be noted, this being
+complicated in some instances by the bearings being insecure, and
+working to an extent which obscures the measurement sought. In such
+cases it is preferable to use a stiff slat lying along the girder, which
+bears, through short blocks over the girder bearings, upon the flanges;
+the deflection is then read by direct measurement of the girder's
+depression at the centre, relative to the slat.
+
+The author is, unfortunately, not able to give any precise information
+on the effect of running-load as against a load that is stationary in
+connection with girder deflections. It is by no means easy in ordinary
+work upon a railway to secure facilities for making such comparative
+tests. It may, however, be confidently stated, as a result of such
+observations as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a 50 feet
+span, but little greater than that due to the same load stationary; it
+may be, perhaps, 5 to 10 per cent. more.
+
+It is evident that to determine the precise difference where the
+quantity to be measured is so small needs apparatus of a more delicate
+character than that in common use, and the control of an engine, or
+engines, for the purpose of making the special tests, conditions which
+on a busy line can only be secured by special arrangements previously
+made.
+
+
+
+
+CHAPTER IX.
+
+DECAY AND PAINTING.
+
+
+The author has collected particulars as to the amount and rate of
+rusting in metallic structures which are of some interest. In all such
+instances it is very necessary to note the conditions which have
+obtained during the process of wasting, as without this, misleading
+conclusions may be drawn. The information given relates in all cases to
+wrought iron, unless otherwise stated.
+
+A plate-girder bridge, having girders under rails, was found to be badly
+rusted. The atmospheric conditions were unusually trying, the air being
+damp and impregnated with acid fumes from adjacent steel works. That the
+wasting was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than those
+farther removed and partly sheltered from the corrosive influence.
+
+The webs were in places eaten right through, having lost a mean amount
+of about 1/8 inch full on each surface in twenty-eight years. Painting
+had not been well attended to.
+
+In a similar bridge, not a great distance from this, but sufficiently
+far away to modify the conditions for the better, considerable wasting
+was also observed, but more particularly where the girders had been
+built into masonry, which, loosening with the constant movement of the
+girder-ends, had allowed moisture to collect, and rust to develop,
+without the chance of repainting these surfaces. The amount of waste at
+the places indicated was, as in the last case, about 1/8 inch on each
+face, and in the same time, other parts of the girders having suffered
+less.
+
+[Illustration: FIG. 58.]
+
+A third plate-girder bridge, with outer main girders, cross-girders, and
+plated floor, carrying a road over a railway and sidings, and which was
+known to have been neglected in the matter of painting, was very badly
+rusted, both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration was, however, the
+smoke and steam from locomotives, which frequently stood for some time,
+during shunting operations, directly under the bridge. The webs of the
+cross-girders, which were originally 1/4 inch thick, had rusted into
+occasional holes during fourteen years--i.e. 1/8 inch from each surface
+in that time. When removed a little later the wasting was so complete
+that it was possible to knock out with a light hammer the remains of the
+web between flanges and stiffeners, so as to leave an open frame only.
+One of the cross-girders was so treated by the men engaged upon the
+work, when it presented the appearance shown in Fig. 58.
+
+In another case--that of a bridge with lattice girders under rails--the
+ends were built into masonry, which had, of course, loosened, with the
+usual result. The air of the locality was certainly pure, but somewhat
+damp. The general condition of the ironwork was good, but end-bars of
+the diagonal bracing, where they had been closed in, had lost 1/8 inch
+on each surface in thirty-three years. The top flanges immediately under
+the timber floor were in a very fair state, which is of some interest
+when it is considered that these were made of steel of the same kind as
+that already noticed as being used in the construction of small girders
+(see Fig. 46, _ante_), described in the chapter upon "High Stress," both
+cases dating from the year 1861. The painting upon the lattice-girder
+bridge had been pretty well attended to; but in the case of the small
+steel girders it had been greatly--perhaps altogether--neglected; this,
+coupled with adverse atmospheric conditions, had produced the result
+that the rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully 1/8 inch on
+each surface, as against a negligible amount under the more favourable
+circumstances.
+
+Girder-work over sea-water, as in piers, seems to rust at a sensibly
+greater rate than inland work under average conditions; but it is hardly
+practicable to make any strict comparison, as in either case the rate of
+oxidation is so much affected--even controlled--by the care bestowed
+upon the structures. This general conclusion is based upon the results
+of examination of wrought-iron girder-work over sea-water of ages
+varying from fourteen to forty-four years. It should be remarked,
+however, that in one case steel girders but five years old, and which
+were frequently wetted with sea-spray, were found to be wasting rather
+badly--the paint refusing to keep upon the surface.
+
+It may be concluded from the above instances, and from others which have
+come under notice, that wrought-iron work, if not properly cared for in
+respect to painting, or under conditions otherwise bad, may be expected
+to rust at a rate which corresponds to the loss of 1/8 inch on each
+surface in from fifteen to thirty years; but with proper care as to
+painting, and exclusive of exceptionally bad conditions, it does not
+appear to waste at any measurable rate. In some instances, upon scraping
+the paint from girders which had been in use for thirty years, the
+author has found, beneath the original red lead, the metallic surface
+bright and clean, showing no trace of rust.
+
+Of ordinary steelwork the same cannot be said, the common experience
+being that mild steel is very liable to be attacked by rust. With
+passable care in the bridge-yard during manufacture, such that with
+wrought iron no after-trouble would be noticeable, steel is very liable
+to show, within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away discloses a
+small rust-pit. This is more often seen on the flange surfaces
+(horizontal) than on web surfaces (vertical), but it is probable the
+position has little to do with the matter, and that it is rather due to
+the fact that rust has been earlier started on the flange-plates, upon
+being put through the drilling-machines and inundated with slurry, which
+occurs only to a more limited extent with webs having fewer holes. The
+heads of steel rivets do not show this tendency to "pit," or to early
+development of rust. The riveting is about the last operation in making
+a girder, each rivet being freed of all rust by heating, and quickly
+coming under the protection of oil or paint. It may happen in this way
+that the heads of rivets on a girder may be exposed without protection
+for as many hours only as the rest of the work for weeks, which fully
+accounts for the difference in behaviour.
+
+The essential point to be observed in all steelwork is to prevent, if
+possible, the first development of rust, for once begun it is much more
+difficult to arrest than in iron; for this reason, oiling of all
+material for a steel bridge, at a very early stage of its existence,
+cannot be too strongly insisted upon. This practice, however, makes the
+work so objectionable, and even dangerous when being lifted--because of
+the liability to slip--to the men engaged upon it, that it is commonly
+very difficult to ensure it being done sufficiently soon to satisfy a
+careful inspector. If the work is carried out under cover, the
+requirement is less urgent. Strictly, all material should be oiled so
+soon as rolled, but the author does not remember to have seen this done
+at any of the mills he has visited, though it is common enough to find
+it specified.
+
+Ironwork does not need the extreme care which should be bestowed upon
+steelwork, but it is desirable that it should be painted as soon as
+possible, the surfaces being first thoroughly cleaned.
+
+There is, probably, for painting girder work nothing to beat good red
+lead as a protective coating; but there is considerable difficulty in
+getting it reasonably pure, without which quality its utility will be
+greatly reduced. The question of purity will, however, be found to be
+largely a question of price. It may be stated broadly that, whether for
+steel or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.
+
+In repainting old work, care should be taken to remove all traces of
+rust previous to laying on the new coat. It is not an altogether
+uncommon practice to repaint old structures by dealing only with the
+parts readily accessible, which, being less liable to rust, probably but
+little need it; leaving those parts which are difficult of access, and
+where rust is developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said, is
+indefensible. It is better rather to neglect the surfaces freely exposed
+and ventilated, and devote the whole care upon those other parts,
+confined and difficult to get at; taking the trouble necessary to remove
+ballast, timber, or whatever may obstruct the operation, in order that
+the bad places may be thoroughly scraped, and then painted. Those parts
+which most need attention may cost, perhaps, to reach--and deal with
+when exposed--ten times as much per yard of surface as the rest of the
+superfices, which needs little, and is always accessible; but the cost
+should not deter the proper carrying out of the work, as it will prove
+the very worst sort of economy to deal with painting in a perfunctory
+manner.
+
+It should be noted that girder work, whether of wrought or cast iron,
+when embedded in lime or cement concrete, or mortar, generally proves to
+be very well preserved, provided that close contact has obtained.
+Cast-iron girders, when carrying jack arches resting upon the bottom
+flanges, are found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of new
+girders. Much the same remarks apply to girders of wrought iron carrying
+jack arches, where protected by the brickwork; provided that the girders
+are sufficiently stiff to minimise deflection, and allow the masonry or
+brickwork to adhere to the surfaces.
+
+Such girders are in a very different condition to those previously
+referred to, in which the ends of the girders, carrying a light floor
+structure, are built into masonry where the deflection slope is
+greatest; though, apart from the few cases where adherence can be relied
+upon, building-in is an undesirable practice, and has the disadvantage
+that after-examination is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted to.
+
+Cast iron has ordinarily--unlike wrought iron or steel--great capacity
+for resisting rust, and will, after many years of absolute neglect,
+appear but little the worse; an advantage which is the more pronounced
+when considered relatively to the greater thickness of the thinnest
+parts in cast-iron girders, the percentage of waste being
+proportionately lessened.
+
+Cast iron does, however, behave somewhat badly in sea-water, the metal
+sometimes losing its original character, and becoming in time quite
+soft; though, if not worn away, as by the attrition of shingle,
+maintaining its original bulk.
+
+Of some forty-five cast-iron piles belonging to various structures,
+examined whilst engaged upon sea-pier work for Mr. St. George-Moore,
+though the author found somewhat diverse results, in no case did there
+appear to be any general softening of the whole thickness, but a
+distinct change for some definite distance inwards, generally to be
+decided without difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of softening was
+found close to the ground, this depth rapidly decreasing higher up,
+till, at a height of 5 feet, but little if any softening could be
+detected. At 2 feet above ground the softening was frequently but
+one-quarter of that at ground level. There was, too, often a
+considerable difference in the behaviour of different piles in the same
+structure under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly none at
+all. For six different structures the amount of softening near ground
+level, of about twenty-five piles examined, was as given in the table on
+the next page.
+
+The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot
+above ground, in a pile thirty-six years old. The decayed material when
+removed was of a soft, greasy consistency, perfectly black, which a few
+hours later was found to have changed to a dry yellow powder, by the
+rapid absorption, it may be supposed, of atmospheric oxygen. It is
+apparent, therefore, from this example that deterioration may proceed to
+a considerable depth; but it should be observed that other piles of the
+set showed softening at ground level of 1/8 inch only.
+
+SOFTENING OF CAST-IRON PILES IN SEA-WATER.
+
+  ---+--------+----------+-----------+----------+---------+---------
+  No.|  Age.  | Maximum  |  Maximum  |Mean Rate | Quality |Materials
+     |        |Softening.|  Rate of  |    of    |of Metal.|Entered
+     |        |          |Softening. |Softening.|         |by Piles.
+  ---+--------+----------+-----------+----------+---------+---------
+  1  |17 years|5/16 in.  |1/8 in. in |1/8 in. in|Soft     |Extremely
+     |        |          |7 years    |15  years |         |soft
+     |        |          |           |          |         |sandstone.
+  2  |36 years|9/16  "   |1/8 in. in |No result |  "      |Rubble
+     |        |          |8-1/2 years|          |         |mound.
+  3  |32 years|3/8   "   |1/8 in. in |1/8 in. in|Moderate-|Fine
+     |        |          |11 years   |15  years |ly hard  |sand.
+  4  |38 years|1/10  "   |1/8 in. in |1/8 in. in|Hard     |Extremely
+     |        |          |47 years   |140 years |         |hard rock.
+  5  |17 years|Small     |Negligible |          |(?)      |Sand and
+     |        |          |           |          |         |Shingle.
+  6  |14 years|Negligible|Ditto      |          |(?)      |Sand.
+  ---+--------+----------+-----------+----------+---------+----------
+
+The least rate of softening noticed, apart from those structures of a
+more recent date, in two of which it was very slight, occurred in a
+pier thirty-eight years old (No. 4), where, of three piles tested, two
+were quite hard, and the third softened 1/10 inch only.
+
+Whatever may be the precise cause of the change, it does not appear to
+be affected by the period or percentage of immersion during the rise and
+fall of tides.
+
+[Illustration: FIG. 59.]
+
+This will be clear from the diagram, Fig. 59, which refers to four piles
+(No. 3 of table), all of the same age, in the same structure. On each
+pile the depth of softening is given at points in strict relation to
+each other, and to the tidal range. The percentages of immersion for the
+various heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening; this,
+indeed, is always greatest near the ground, at whatever actual height it
+may be. For instance, pile A was at ground-level softened 1/4 inch,
+that point being 60 per cent. of its life under water; but on pile B, at
+a point 74 per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level of
+this pile, the percentage being there 87, the softening was no greater
+than at ground-level at pile A.
+
+It is probable that while the percentage of submersion in moving water
+hardly appears to affect the result, yet prolonged contact with wet
+sand, sea-weed, or clinging shell-fish may do so. This seems to suggest
+that the process of change, as between the sea-water and the iron, is
+slow, and to be effective must be continuous; so that it is only found
+to any considerable extent where the water in contact with the surface
+is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1
+foot and 6 inches above ground-level, the surface was in one pile
+shrouded in a thick mantle of heavy sea-weed, and in the other covered
+by molluscs; in both instances the surfaces being thus kept moist and
+undisturbed. The piles of the fourth case were in hard rock, were clean,
+and, where accessible, always either in moving water or quite dry.
+
+However this may be, the power to resist softening certainly appears to
+vary largely with the quality of the iron. The piles, referred to above,
+in which deterioration proceeded at the most rapid rate were certainly
+of a soft metal, the first being markedly so. On the other hand, certain
+piles (No. 4) of hard, close-grained iron suffered very little.
+
+It may be mentioned with respect to the last named, as a matter of
+interest, that the caps of the lower lengths (just above ground-level)
+had been cast with short pieces of wrought iron projecting--possibly for
+lifting purposes--which during thirty-eight years had altered in
+character to something very like softened cast iron, but laminated, and
+harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained
+having the semblance of wrought iron. The percentage of submersion was
+about 60.
+
+A number of piles, not included in the table, varying from fifteen to
+forty-four years old, and of the same structure to which set No. 2
+belonged, were all found to be hard, with the exception of one showing
+3/16 inch of softening. These are omitted, because the mud surrounding
+them was at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points testing might
+have disclosed different results. It is probable that for any piles
+standing in soft material examination below the surface would reveal
+more pronounced softening than where occasionally exposed.
+
+To meet the effects of sea-water on cast-iron piles, and for other
+reasons, it is a common and good practice to make the lower lengths of
+greater thickness--say, 3/8 inch more--than that sufficient for the
+upper. Occasionally, also, the bottom lengths are filled with concrete,
+which no doubt adds to the length of time during which they may be
+relied upon.
+
+
+
+
+CHAPTER X.
+
+EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+
+In the preceding chapters defects of various kinds to which riveted
+bridgework is liable have been more particularly dealt with; it is now
+proposed to consider the examination of such structures, following this
+by a reference to methods of repair and strengthening, leaving the
+treatment of other classes of bridgework to be developed under their
+proper headings, though some of the remarks immediately following will
+apply to all.
+
+The exhaustive survey of a bridge is only to be made after considerable
+experience in the work, but it may be stated that in looking for defects
+it is well to seek where they are least expected, till, with practice,
+one knows better where to direct attention. When examining with a view
+to pronouncing an opinion upon the fitness of the structure to remain in
+place, if in any real doubt, it is wise to give a casting vote against
+it; and finally it may be said that upon taking down a bridge condemned
+for any one or more defects, it should be examined for worse. This may
+seem to be somewhat pessimistic, but is based upon the teachings of
+experience.
+
+Preliminary examination of a bridge may reveal such faults or weaknesses
+as at once to ensure its condemnation; but if this is not the case, and
+there is a reasonable probability that the structure may be given a
+fresh lease of life, it will, for the purpose of estimating the
+strength, or for possible repairs, commonly be desirable to secure
+precise particulars of the existing structure independently of any
+drawings that may be in existence, and which will very probably be
+incorrect, the finished work, if old, seldom agreeing with the contract
+drawings. A final decision may in this case be deferred till after the
+measuring up has been completed, the condition of the structure becoming
+more familiar in the process.
+
+It is desirable first to ascertain whether the bridge remains in good
+form, whether the camber of girders appears to be what might be
+expected, or agreeable with existing records, though much reliance must
+not be placed upon figured cambers, it being quite common for girders to
+leave the bridge yards with the camber something other than that
+intended. The deflections under live load will also be observed, and
+compared with the calculated result, or checked by judgment. The
+calculations upon which strength and deflections are based will, of
+course, refer to the actual sections, which are sometimes a little
+difficult to ascertain if there has been irregular rusting. In
+continuous girders also, levels having been taken, allowance should be
+made for effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the like object. It
+is seldom that the main flanges of girders show signs of weakness,
+unless from flexure in the case of long and narrow top members,
+insufficiently stiffened; but there may be want of truth from other
+causes already dealt with. In plate girders the webs should be most
+carefully scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange angles, if the
+floor rest upon the flange. All riveted connections, of course, need
+close attention, both for straining effects, where there is a liability
+to wracking, and to detect loose rivets. Loose rivets and want of
+tightness in other parts of the work may frequently be detected at
+sight by a reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects of weather;
+it may be seen round rivet-heads or along the edges of angle-bars, or
+other parts where there is movement. Loose rivets, though generally to
+be detected also by the hammer, may perhaps in the case of thin-webbed
+cross-girders be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may sometimes be
+detected by simultaneous deflection tests--with rods--at the top and
+bottom flanges of a girder, at the same distance from the bearings. Any
+difference in the readings may indicate loose web-rivets, or possibly a
+tear in the web running parallel to the flange angles.
+
+Bracings between girders are very apt to display a rich harvest of
+working rivets. Cross-girders and longitudinals also may have loose
+rivets at their connections, and be very badly wasted, with quite
+possibly cracks in the webs, or other defects already enlarged upon.
+
+The condition of the road upon the bridge will frequently be an
+indication of the state of the floor which carries it; or the existence
+of rail-joints which are working badly may very properly lead to a
+critical examination of the girder-work immediately below, as this is a
+fruitful source of damage in light constructions. Floor-plates, where
+these exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the latter
+being often loose and unsatisfactory.
+
+Trough floors may be expected to show loose rivets near the ends, with a
+probability of excessive leakage where they abut against the webs of
+supporting girders.
+
+Floor plates resting upon abutments or piers, being very liable to
+serious decay, require attention, and girder-work entering masonry
+should receive close scrutiny, any obstruction to a sufficient
+examination being removed so far as is judged sufficient for the
+purpose. The structure should, of course, be closely watched during the
+passage of live load for any signs of abnormal movement, excessive
+vibration, or lurching.
+
+In addition to seeking for these various defects, or others which have
+been referred to in these pages at length, it will be well always to be
+alive to the possibility of faults to be seen for the first time, or of
+which the author has furnished no instance.
+
+Having formed a reliable opinion as to the state of the bridge, this, if
+satisfactory, may leave to be determined only the question of strength
+relative to the loads carried. It is apparent that stress limits
+suitable for a new structure, which has all its life before it, of
+purpose moderate to cover possible deteriorations, the growth of loads,
+and other adverse influences, may to avoid immediate reconstruction,
+reasonably be permitted of a higher value for a further term of years in
+the case of a structure which it is known has for a considerable period
+behaved well, and remains in good condition. What this higher value may
+be will be greatly influenced by the circumstances of each case, and,
+being largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the nominal unit
+stress in an old bridge may be a very considerable amount in excess of
+that allowed for new work, without, of necessity, showing any ill
+effects; and the author is of opinion that for old bridges in good
+condition it is quite prudent to allow an excess of 33 per cent. beyond
+that permissible for a new design. If the structure is too weak to
+satisfy this modified condition, it may be possible to bring it within
+the stress limit by a reduction of ballast or other removable dead
+weight. If this expedient does not promise to be satisfactory, or the
+bridge shows actual signs of weakness, or palpable defects, it will be
+necessary to deal with the question of repair, strengthening, or
+reconstruction.
+
+The repair of built up bridgework resolves itself largely into a matter
+of replacing loose rivets by cutting these out, rhymering the holes, if
+desirable, and again riveting. It will often be sufficient to do this
+with no particular precautions as to bolting up temporarily; the rivets
+having been loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to remove all
+the rivets, bolting up securely as this is done, in order to make a
+tight job, taking out each bolt in turn as required, and again filling
+the holes; or it may be well in a bad case first to remove all loose
+rivets, substituting good bolts, in order that work which has gone out
+of shape owing to defective rivets may first be brought true.
+
+Cross-girder webs, cracked vertically or nearly so, are commonly
+repaired with splice-plates on either side; but in doing this it is
+undesirable to add plates of excessive thickness relative to the
+web--probably poor--as by an abrupt change of web section it appears not
+unlikely a fresh break may be favoured.
+
+[Illustration: FIG. 60.]
+
+[Illustration: FIG. 61.]
+
+[Illustration: FIG. 62.]
+
+[Illustration: FIG. 63.]
+
+Replacing wasted flange-plates, or adding new plates to those which
+exist, is occasionally resorted to in the case of main girders, the
+flanges of which are sufficiently accessible, but the operation is
+difficult, takes some little time, and should only be attempted under
+the constant supervision of a thoroughly capable man. When done, if the
+girder has not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the new section,
+the old always taking more by the amount of the dead-load stress
+previously carried. The method which the author has seen applied to
+lattice girders of about 80 feet span, having good angle-bars in the
+flanges, with a shallow vertical web for attachment of diagonals,
+consisted in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been removed.
+The new plate length having been prepared, was, on a Sunday, during a
+few hours' cessation of traffic, marked off, the temporary bolts being
+removed for the purpose, and then replaced. After the plate had been
+drilled, on a later Sunday, it was finally put into position, bolted up,
+and riveted at leisure; cover-plates make additional trouble, but are
+dealt with on the same principle. The method as shown in Fig. 60 is,
+however, barely practicable for so many plates. It is preferable, if it
+is proposed to add section, to do this with as little interference as
+possible with existing rivets of importance. This may be accomplished,
+if the existing plates are not too wasted at their edges, by riveting on
+new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength
+of a girder is increased by the addition to the top or bottom boom of
+material in such a form as sensibly to increase the depth, and thus,
+while adding increased section to one boom, to reduce the stress in
+each, though to dissimilar amounts. By this device also the relief is
+effective only as regards the live-load stress; under dead load only the
+new material does no work, provided, of course, that no relief staging
+was used during the alterations. For girders carrying any considerable
+proportion of dead load the method is very inefficient, though for
+others, in which the live load is relatively large, the result should be
+more satisfactory.
+
+As this question of adding new section to old is of much importance in
+dealing with repairs and strengthening operations, a few general remarks
+upon the subject will be pertinent. The difficulty in such work commonly
+is to cause the new to render any considerable assistance to the old in
+those cases which occur in practice. If a bar be imagined under
+longitudinal stress varying between 0 and a maximum, then, if the area
+of the piece be increased at the time when it takes no stress, its
+capacity for resisting the maximum amount will be increased, and for
+added material of similar elasticity the unit stress proportionately
+reduced. If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any degree.
+To take a third case, of the maximum being twice the minimum load, it
+will be necessary, in order to lower the maximum unit stress by 25 per
+cent., to double the original section of the bar if, as supposed, the
+extra metal has been added to the piece when under the smaller load, so
+that the new section is only effective in assisting to carry the
+remainder of the load at such times as it may be imposed. The
+relationship stands thus:--
+
+      Live load         New area
+  ---------------- � -------------- = relief.
+  Live + dead load   New + old area
+
+These statements will be true under the conditions named, within the
+elastic limit of the material; but some advantage would be derived in
+the second case, and a more marked benefit in the third, if the load
+assumed to be a maximum were exceeded, or if the composite bar were
+tested to destruction; as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment as to how
+far this reserve of strength may be considered of value.
+
+If, instead of simply adding section to the bar, some part of the
+constant load is put upon the new section by the manner of attachment,
+the combination will, of course, be more effective.
+
+To apply these considerations and illustrate the way in which the two
+methods of adding flange section work out when reduced to figures, the
+case will be supposed of a girder 6 feet deep, carrying a load of which
+one-third is dead and two-thirds live. To the flanges of this girder are
+added plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the girder before
+strengthening is liable, the depth remaining substantially unaltered.
+With dead load only the original section would be stressed to 2�3 tons
+per square inch, the new section being then unstressed. Under full load
+the new and old material take 3�1 tons per square inch additional,
+making the modified stress on the original section 5�4 tons per square
+inch, as against 7 tons; or a reduction of 22 per cent. This compares
+with 33 per cent., the relief due to 50 per cent. increase of flange
+area under ordinary conditions of stress distribution.
+
+Let the second method of strengthening the girder now be considered,
+using, for purposes of comparison, the same total amount of new material
+to increase the girder depth by an addition to the top flange. This
+section will be equal to the area of one flange, which, though it may
+be applied in many different ways, giving a greater or a less increase
+to the depth, would probably be used in some such manner as that shown
+in Fig. 64, increasing the effective depth for live-load stress by
+nearly 10 inches.
+
+[Illustration: FIG. 64.]
+
+The added material will, as in the previous case, leave the dead-load
+stress unaltered, or 2�3 tons per square inch. The stress in the bottom
+flange due to live load will, however, now be 4�1 tons per square inch,
+making a total stress of 6�4 tons per square inch, against 7 tons--the
+original stress. The reduction here is 8 per cent. only, as compared
+with 12 per cent., the relief due, under ordinary conditions, to an
+increase of effective depth from 6 feet to 6 feet 10 inches, and by the
+use of additional material, equal, as before, to one-half of the total
+flange areas before the alteration.
+
+The effect on the top flange need not be here gone into in detail, but
+it may be said that, owing to the increase of gross section and of
+depth, the ultimate stresses of both the new and old material are
+greatly less than as given for the bottom flange.
+
+Girders strengthened by the first of these two methods would, it is
+probable, if tested to destruction, give results more nearly in accord
+with the actual percentage increase of flange section, plastic
+deformation of the metal, before failure, tending to reduce the
+differences of stress on the new and old material of the sections.
+
+[Illustration: FIGS. 65 and 66.]
+
+Web members of lattice girders may, if weak, sometimes be dealt with by
+the introduction of supplementary bars, parallel to and between the old
+members, or by the addition of strips or angles to the existing
+diagonals. The treatment will be largely influenced by the nature of the
+old detail, which may lend itself to some one arrangement much better
+than to any other.
+
+End riveting of web members may, if it has become loose, be dealt with
+by simply rhymering the holes a size larger, and re-riveting in the best
+manner, if the stresses are not excessive; or it may be necessary to
+devise some additional attachments by which new rivets are brought into
+use (see Figs. 65 and 66). The effective relief due to supplementary
+rivets will be influenced by similar considerations to those governing
+increase of section.
+
+[Illustration: FIG. 67.]
+
+[Illustration: FIG. 68.]
+
+Old structures are very frequently deficient in bracing, which may, in
+such cases, be advantageously introduced; or girders individually weak
+may be rendered collectively efficient by suitable bracing. In
+considering the advisability of this, however, the case should be viewed
+with regard to the possible effects of such members, as already dealt
+with in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders may have
+the effect, under live load, of increasing the stress on the outer
+girders due to twisting of the structure as a whole, though the inner
+girders will, except for full loading of the whole bridge, be advantaged
+as to stress values, and in any event bettered by being held up to their
+work. The effect upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations the
+detail should be schemed with special care to ensure simplicity in
+execution, smith's work being rigorously avoided. A good arrangement for
+supplementary bracing between plate-girders, which gives little trouble
+in carrying out, is shown in Fig. 67; or where the stiffeners of such
+girders are in line across the bridge, the detail given in Fig. 68 may
+involve less expenditure. Difficulties may be experienced in riveting,
+unless great care is taken in the positioning of rivets. Fitting-bolts
+are only to be relied upon as such, if they really justify the name;
+they are, though easy to specify, by no means easy to secure under the
+conditions of practical work. Weak cross-girders may make
+alterations--in some cases considerable--necessary, to rectify the
+defect of strength. The removal of old girders to make room for new is
+seldom resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders between the
+old in cases where there is no plated floor to make the work difficult.
+By this method there is, of course, an increase of appreciable amount in
+the dead load carried by the main girders, which would in many instances
+be objectionable. With deep and heavy main girders, having plate webs,
+cross-girders may be strengthened by improving the end connections by
+suitable gussets, and attachment to good vertical stiffeners, the fixity
+of the ends thus aimed at being assured by overhead struts or girders,
+from one main girder to its fellow, at intervals apart well considered
+with reference to the horizontal strength of the top flanges, the whole
+thus making a closed frame, as shown in Fig. 69. The method appears
+feasible, but it should be stated that the author has not known it to be
+applied in its entirety as a means of strengthening an old floor.
+
+[Illustration: FIG. 69.]
+
+A simple and very common device consists in substituting for the
+ordinary cross-sleeper road, where this exists, stout timber
+longitudinals under the rails, which have, where the cross-girders do
+not exceed 5 feet centres, a marked distributive effect, tending to
+reduce the maximum load upon any individual girder. With a similar
+object, trough girders containing longitudinal timbers are sometimes
+adopted where the depth available is not enough to enable sufficiently
+stiff timbers to be used alone. In either case the object sought is the
+same--to modify the effect of the heavier wheel loads upon isolated
+cross-girders. When the spacing is so close as 4 feet, the beneficial
+result of this treatment is considerable, but at 8 feet centres it can
+have but a moderate effect where timbers alone are used.
+
+Occasionally, for long cross-girders, a distributing girder is placed,
+with the same intent, in the 6 feet way, its function being limited to
+this use only if the depth and strength are sufficiently small to serve
+this object alone, as distinct from the case in which it becomes a
+carrying girder transferring load to the abutments. As a distributor
+simply, the girder has to equalise the bending moments amongst the
+cross-girders, to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous to
+alteration, for a position of the wheel loads such that the heaviest
+comes upon a centre cross-girder, the mean of these moments will, when
+compared with that for each girder, show the difference to be induced as
+a result of introducing the distributor. These differences of moment
+render necessary at the centre of the cross-girders reactions upwards or
+downwards, as the case may be, of amounts competent to induce moments
+below the inner rails equal to these differences.
+
+It is these reactions which must be provided by the distributing girder
+at a moderate stress, and without flexure of such an amount as sensibly
+to modify the reactions. The greatest section necessary at any one point
+may then be adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no harm in a little
+excess in a case of this kind, the total cost being but little affected
+by some small addition to the weight, where labour upon the site is so
+considerable an item as in work of this description. The ends of the
+distributing girder should be carried on to the abutments or piers to
+ensure adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at an early
+stage, by boning or by levelling, the condition of the cross-girders as
+to uniformity of heights, as this may affect the length most suitable
+for separate sections. Between the underside of the distributor and the
+cross-girder tops there will commonly be spaces of varying amounts,
+which should be filled by packings to fit, rather than by pulling the
+work together by force, introducing undesirable stresses of uncertain
+amount.
+
+In the earlier remarks upon the strengthening of bridgework by the use
+of new material, it has been assumed that the modulus of elasticity of
+the new metal is similar to that of the old; it may, however, as in
+cases where wrought-iron work is reinforced by additions in steel, be
+necessary to take the difference of elastic properties into account,
+with which object the new section should be multiplied by a quantity
+(greater or less than unity) inversely proportional to the higher or
+lower modulus of the new material, that is to say, by
+
+  E of old material
+  -----------------
+  E of new material
+
+
+
+
+CHAPTER XI.
+
+STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+
+The addition of distributing girders, described in the last chapter, as
+a means of strengthening a bridge floor, while sufficient in many cases
+so far as the cross-girders are concerned, does not in any appreciable
+way assist the main girders. When for a two-line bridge, having outer
+main girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders may be used,
+placed either above or below the cross-girders, on the centre line of
+the bridge.
+
+There are two principal ways in which such a girder may be brought into
+use; the easier, but generally less economical, is by making a simple
+attachment to the cross-girders, the old girder work still taking the
+whole dead load. By this method the new girder does no work but carry
+itself till the live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the second
+method is to make the connection adjustable, so that a part of the floor
+weights may be imposed upon the new girder as an initial load. In doing
+this the old outer girders will rise slightly, being relieved of stress,
+and the cross-girders also lifted at the middle, whilst the new girder
+is depressed as the load is brought upon it. With some part of the live
+load a very considerable proportion of the total may in this way be
+carried by a centre girder of moderate section. The whole question, by
+either method, turns upon deflections; and it is in determining the
+relative movements of the girders that the problem chiefly lies.
+
+It is convenient first to determine the percentage of load relief to be
+effected in the main girders, as to which it is to be observed that as
+this relief (distributed) is induced by the upward reaction of the new
+girder acting at the centre of the cross-girders, the stress relief of
+these will, as a rule, greatly exceed that of the outside girders. For
+the generality of cases, it may be taken that the relief suitable for
+the outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress in these
+to a greater degree.
+
+If, however, it be thought desirable to check this, it may be done by
+considering a cross-girder subject to its dead and live loads acting
+downwards, and to reactions at the centre and ends. At the centre the
+reaction will be the load of which the two main girders are relieved on
+a length equal to the pitch of the cross-girders, or as here given:--
+
+  _c_ � _t_ � P = reaction at centre (1)
+
+_c_ being the percentage of relief; _t_ the total load per foot run of
+the bridge; and P the pitch of cross-girders. The live loads carried by
+the cross-girders are for this purpose taken at per foot run, as for the
+main girders. With these data it will be easy to construct a diagram of
+moments, making it evident whether the relief proposed for the main
+girders will give a sufficient percentage of relief to the floor beams.
+
+Granting that this proportion has been decided, and dealing first with
+the case in which the centre girder is simply attached to the
+cross-girders, and takes no dead load other than its own weight, then
+the live load carried by the outside girders, and previously borne
+wholly by them, will be reduced by the amount it is intended to transfer
+to the centre girder, and will become
+
+  L{_l_} - (_c_ � L{_t_}) = live load on outer girders (2)
+
+L{_l_} being the total live load, and L{_t_} the total dead and live
+load carried by the bridge. From this the deflection of the outer
+girders corresponding to this modified live load may be derived.
+
+[Illustration: FIG. 70.]
+
+It is next necessary to ascertain the vertical movement, commonly a
+depression, of the cross-girders at the centre relative to their ends,
+when subject to the running load only, and supported at the middle and
+ends, the centre reaction being obtained as before indicated (1). This
+movement will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the upward
+flexure of the girder due to the centre reaction, considered as separate
+effects. Stress values having been estimated for the two conditions,
+these results may readily be deduced by simple flexure formul�,
+observing that while the curve of moments due to live load sufficiently
+approximates to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter "Deflections,"
+the flexure due to the centre reaction will be but 0�80 of that which
+corresponds to the same stress for distributed loading. Or, the curve
+assumed by the girder under live load may be plotted by a method to be
+later explained.
+
+The sum of the movements now determined--that is, the live-load
+deflection of the outer girders, and depression, as is commonly the
+case, of the cross-girders--will give the extreme depression (marked _m_
+in Fig. 70), from the dead-load condition of the middle cross-girders,
+when supported to the extent desired by a centre girder whose
+proportions are not yet known, but which, carrying the required
+percentage of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the flanges of the
+new girder, governed by this flexure, will for a plate girder be
+
+  D � C � _m_
+  ----------- = _f_, unit stress on gross section (3)
+       S�
+
+D and S being, as before (see "Deflections"), the depth and span
+respectively in feet, C a constant, _m_ the deflection in inches, and
+_f_ the stress per square inch on the gross section of flange.
+
+The gross area A, of the flange, is given by
+
+  S � _c_ � L{_t_}
+  ---------------- = gross area of flange (4)
+    8 � D � _f_
+
+_c_ � L{_t_}, being, as in (2), the load transferred to and carried by
+the centre girder.
+
+The actual stress in the flanges will, of course, be greater by an
+amount due to the girder's own weight; but this does not affect the
+question of relief. For any ordinary case the stress per square inch
+will be low; but it will manifestly be useless to assume a greater
+stress with a view to economy, as the effect of reducing the section
+will simply be to make the girder too flexible, thus causing it to be
+less effective than primarily intended. If, as is seldom the case, there
+is freedom as to the depth of girder permissible, it is evident the unit
+stress may be made a condition, and the depth deduced by a suitable
+modification of formula (3); the relief desired being in this way
+equally well assured. Indeed, in the rare instances in which any depth
+may be adopted, this method is--contrary to the general rule--distinctly
+economical, particularly if the girder may be placed below the
+cross-girders, which simply rest upon it, without elaborate attachments.
+
+[Illustration: FIG. 71.]
+
+Considering now the second method of applying centre girders by which
+the new girder is made initially to carry part of the dead load, by
+adjustment, it will at once be recognised as a more complex matter. The
+measure of relief by which the old girderwork shall benefit need not be
+affected by the method of applying the centre girder, and may be decided
+on the principles already considered. The outer girders carrying a
+reduced load, when the bridge is fully loaded, and the cross-girders
+being in part supported at their centres in the manner already
+described, will give a resulting depression _m_ (see Fig. 71) of the
+centre cross-girders, below the original dead-load position, of a
+similar amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre girder, which may
+be designed to carry the required percentage of the total bridge loads
+with the maximum stress and depth, as conditions, leaving the initial
+dead load and necessary adjustments to be ascertained. This is the
+common case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.
+
+The centre girder of fixed depth being then required to carry a definite
+load at a definite flange stress, will deflect a definite amount at this
+stress. If this deflection equalled the extreme depression _m_ of the
+old girder work, no adjustment would be necessary, the centre girder
+then carrying no initial dead load, as by the first method; but for
+centre girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally being small,
+and in order to ensure that the new girder shall do its full work, some
+dead load must be put upon it. In the act of adjustment the
+cross-girders must be lifted and the centre girder depressed, till the
+joint movement equals the excess _s_ of the centre girder deflection
+over _m_, when the new girder will carry the proper amount of initial
+load, and upon further deflection under live load give the full measure
+of relief. The amount of "lift" or upward flexure of the old girder
+work, and the depression or "drop" of the new girder, during adjustment,
+will depend upon relative stiffness, and may be ascertained as
+follows:--
+
+For unit reactions at the centre of the cross-girders the upward flexure
+of these may be ascertained, as also the upward flexure of the two outer
+girders when subject to forces of the same total amount (one-half to
+each) applied at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are subject to
+unit lifting forces; similarly, the depression of the centre girder for
+unit loads applied at the cross-girders may be determined. There will
+then be known the movements upwards and downwards of the old and new
+work when being drawn together by unit forces applied as stated.
+
+If
+
+  _l_    = lift due to unit loads,
+  _l{t}_ = total lift due to adjustment,
+  _d_    = drop due to unit loads,
+  _d{t}_ = total drop due to adjustment,
+  _s_    = deflection excess = gross adjustment,
+
+there will then be
+
+     _d_
+  --------- � _s_ = _d{t}_,
+  _l_ + _d_
+
+total drop of centre girder under adjustment,
+
+     _l_
+  --------- � _s_ = _l{t}_,
+  _l_ + _d_
+
+total lift of centre cross girders under adjustment,
+
+  _d{t}_
+  ------ � unit load =
+   _d_
+
+initial load put upon centre girder at each cross-girder.
+
+The rise of the two outer girders for upward forces together equal to
+those depressing the centre girder may readily be deduced.
+
+[Illustration: FIG. 72.]
+
+[Illustration: FIG. 73.]
+
+The act of adjustment may conveniently be effected by the arrangement
+shown in Fig. 72, in which each cross-girder is hung up at its centre by
+four bolts. At the middle of the centre girder the total amount to be
+screwed up will be that corresponding to the deflection excess _s_, but
+towards the ends this amount decreases, and may advantageously be
+represented by a diagram as Fig. 73, in which, if _s_ represents to
+scale the amount to be screwed up at a centre cross-girder, the
+corresponding amounts for other girders may be read off direct. It will
+be apparent that it must be necessary to place the centre girder at
+such a height as to leave a space between the old and the new work
+greater than the amount to be screwed up, this excess clearance being
+ultimately filled by a packing.
+
+The precautions to be observed in carrying out this kind of work, and
+the practical methods of adjustment adopted by the author after some
+little experience, may here be given.
+
+Great care is necessary at the outset to ascertain the true spacing of
+the cross-girders, to ensure that the bolt-holes in the bottom flange of
+the centre girder shall come where desired. The fixing of the
+cross-girder brackets also needs close attention to avoid after trouble,
+the bolt-holes in the brackets being preferably drilled on the site
+after fixing. It will, for masonry abutments, be necessary to fix
+bedstones to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps leave the
+stones liable to settle slightly when the full load is carried. To
+eliminate the bad effect of this upon the ultimate adjustment, and to
+take up any initial set of the new girder work, which would be
+prejudicial in the same way, it is desirable, the centre girder being in
+place, to screw up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it is
+convenient to prepare, for use at the bridge, a diagram somewhat similar
+to Fig. 73, giving the amount by which the new and old work are to be
+brought together at each cross-girder, with the number of turns for each
+nut to effect this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is repeated as
+often as necessary, and so managed as to bring all up proportionately to
+the final requirement, keeping tally with chalk marks over each
+cross-girder as a check. The preliminary screwing up should be conducted
+with little less care than that adopted for the later adjustment, to
+avoid damage to the old work. This later adjustment having in due course
+been effected, it is then necessary to measure for packings to fill the
+spaces remaining between the old cross-girders and the new centre
+girder. These spaces should be callipered at each of the four corners,
+care being taken to avoid after-confusion. The measurements ascertained
+will, however, be too great for the finished packings, as an allowance
+of not less than 1/10 inch (total), will commonly be wanted to cover
+irregularities in the surfaces. The packings, having been prepared and
+checked, may be slipped into place after slacking all the bolts a small
+amount to permit this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last operation.
+
+As a check upon the calculations and adjustment, the "lift" of the outer
+girders and cross-girders, and the "drop" of the centre girder may be
+observed by levelling. For this purpose the author has used a staff of
+inches divided into tenths, with which, and a good level, very accurate
+readings may be taken for short distances.
+
+No reference has been made to the effect of skew in a bridge on the
+above methods, the explanation given applying rather to bridges square
+on plan. The influence of skew on the load distribution will largely be
+a matter of detailed calculation. The flexure of the girders may also be
+sensibly affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to modify the
+amount of screwing up during adjustment, which may be better understood
+by reference to Fig. 74, and comparing it with Fig. 73, the adjustment
+diagram for a square bridge.
+
+To illustrate how these methods of strengthening work out, and compare
+as to weights of centre girders required, the case has been assumed of a
+wrought iron bridge of 60-feet span, having outer girders 5 feet deep,
+of 39 square inches gross flange area; and cross-girders, at 8-feet
+centres, 27-feet span, 1 foot 9 inches deep, with a gross flange area of
+twenty square inches. The dead load and live load on either road are
+each 1�75 tons per foot run.
+
+The stress in the outer girders previous to the alteration being 6 tons
+per square inch gross, it is desired to relieve this to the extent of 33
+per cent. by a steel centre girder. In the table here given the
+quantities given in italics are fixed as primary conditions:--
+
+CENTRE STRENGTHENING GIRDERS FOR 60-FT. SPAN.
+
+  ----------------------------+-----------+------------+------------
+                              |  Centre   |  Centre    |
+                              |  Girder,  |  Girder,   |Adjustments
+              --              |  Stress   |   Depth    | Unknown.
+                              |  Unknown. |  Unknown.  |
+  ----------------------------+-----------+------------+------------
+       _Outer Girder._        |           |            |
+                              |           |            |
+  Deflection under modified   |           |            |
+  live load                   |  �42 in.  |  �42 in.   | �42  in.
+  Lift of adjustment          |   _nil_   |   _nil_    | �153  "
+                              |           |            |
+      _Cross Girders._        |           |            |
+                              |           |            |
+  Depression under live load  |           |            |
+  --modified conditions of    |           |            |
+  support                     |  �13 in.  |  �13 in.   | �13   "
+  Extreme depression (_m_)    |  �55  "   |  �55  "    | �55   "
+  Lift of adjustment (cross-  |           |            |
+  girder only)                |   _nil_   |   _nil_    | �095  "
+  Total lift of adjustment    |           |            |
+  (_l{t}_)                    |   _nil_   |   _nil_    | �248  "
+                              |           |            |
+      _Centre Girder._        |           |            |
+                              |           |            |
+  Depth                       | _3�5 ft._ |  8�2 ft.   |_3�5 ft._
+  Unit stress on gross section|           |            |
+  (ex girder's weight)        | 2�14 tons | _5�0 tons_ |_5�0 tons_
+  Total deflection (ex        |           |            |
+  girder's weight)            |  �55 in.  |  �55 in.   |1�28 in.
+  Deflection excess (_s_)     |   _nil_   |   _nil_    | �73  "
+  Depression, or "drop" of    |           |            |
+  adjustment (_d{t}_)         |   _nil_   |   _nil_    | �482 "
+  Gross area of flange        |105 sq. in.|19�2 sq. in.|44�5 sq. in.
+  Weight                      |  20 tons  |  10�4 tons |11�4 tons
+  Net flange stress (including|           |            |
+  girder's weight)            | 3�19 tons |  6�87 tons | 6�94 tons
+  ----------------------------+-----------+------------+------------
+
+Girders subject to distributed load are treated as having uniform
+stress, but where this is not strictly the case, as in some light
+girders, it will be necessary to take the fact into account. For centre
+girders of wrought iron, and a unit stress on the gross section of 4
+instead of 5 tons, the girder weights are between 9 and 10 per cent.
+greater.
+
+[Illustration: FIG. 74.]
+
+In the above treatment of the application of centre strengthening
+girders there is a source of error which should be touched upon. If,
+under live load, the centre girder deflects more than the outer girders,
+as it commonly will, there must be a want of uniformity in the behaviour
+of the cross-girders, those near the abutments being more relieved than
+the estimated amount of relief of those at the centre, which will have
+less than that intended; but the reduction of stress in the
+cross-girders will generally be so considerable that any such ambiguity
+of excess or defect is commonly unimportant; the effect of this also
+upon the main girders is much less than might be supposed, being, for
+the third of the cases just given, about 2-1/2 per cent. excess for the
+centre girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as approximate only.
+It is possible to eliminate some part of the error by lifting the end
+cross-girders during adjustment, a less amount than that given by the
+diagrams, Figs. 73 and 74, taking care that the centre girder is
+depressed its full amount by lifting the centre cross-girders a little
+more; this refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.
+
+Particulars are here given of five ordinary cases, comparing the
+calculated and observed results of adjustment. The operation of
+levelling was conducted by a quick-eyed and capable assistant, who was
+not made acquainted with the results expected, in order to avoid any
+sub-conscious tendency to match the calculated figures:--
+
+EXAMPLES OF CENTRE GIRDER ADJUSTMENTS.
+
+  ---------------------------------------+-----------+-----------------
+                    --                   |Calculated.|    Observed.
+  ---------------------------------------+-----------+-----------------
+                                         |   in.     |    in.
+                                         |           |
+                          No. 1.--56-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   �82     |    �84
+  Lift of cross-girders at centre        |   �23     |    �22
+  Lift of outer girders                  |   �20     |�10 and �13
+                                         |           |
+                          No. 2.--57-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   �50     |    �50
+  Lift of cross-girders at centre        |   �18     |    �20
+  Lift of outer girders                  |   �11     |�08 and �10
+                                         |           |
+                          No. 3.--67-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   �70     |    �75
+  Lift of cross-girders at centre        |   �15     |    �17
+  Lift of outer girders                  |   �10     |    �09
+                                         |           |
+                          No. 4.--68-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   �70     |    �65
+  Lift of cross-girders at centre        |   �20     |    �18
+  Lift of outer girders                  |   �13     |    �14
+                                         |           |
+            No. 5.--52-_Ft. and_ 28-_Ft. Spans continuous._
+                                         |           |
+                                         |Long |Short|Long |Short
+                                         |Span.|Span.|Span.|Span.
+  ---------------------------------------+-----+-----+-----+-----------
+                                         | in. | in. | in. | in.
+  Depression of centre girder            | �28 | ..  | �29 | ..
+  Lift of centre girder                  | ..  | �04 | ..  | �03
+  Lift of cross-girders (centre of spans)| �17 | �09 | �15 | �13
+  Lift of outer girders                  | �08 | ..  | �08 | ..
+  Depression of outer girder             | ..  | �01 | ..  |negligible.
+  ---------------------------------------+-----+-----+-----+-----------
+
+The method of calculation adopted for these cases was not precisely that
+given, though depending upon the same broad principles. The first cannot
+be considered a good example. The last, having continuous girders, of
+course needed special treatment.
+
+Of about seventeen bridges strengthened in the manner described, the
+effect generally was satisfactory, in reducing deflection and vibration;
+but in two cases of small span, owing probably to settlement of
+bedstones, the results were not so good.
+
+From first to last the work of putting in a centre girder takes some
+little time, owing to the slow progress generally made in fixing the
+brackets, preparing packings, etc. The cost of a typical case was about
+23 per cent. of the cost of a new superstructure, with a 30 per cent.
+relief of stress.
+
+[Illustration: FIG. 75.]
+
+[Illustration: FIG. 76.]
+
+A special case of strengthening by a centre girder, having considerable
+interest, may be here referred to. The primary idea involved was not the
+author's. The bridge dealt with has already been noticed under "Bracing"
+and a section, before alteration, shown in Fig. 26. The span being 85
+feet, there was no room for a centre girder of sufficient depth above
+the cross-girders and between the roads, nor was it considered
+economical to place the girder wholly below the floor, because of the
+costly staging this would have necessitated for erection purposes, the
+height above ground level being very great. A girder was therefore
+designed, having open latticing at an angle of 60 degrees, with a bottom
+boom to be below the cross-girders, the top being as high above the
+rails as could be permitted (see Figs. 75 and 76). A temporary boom was
+arranged at the intersection of diagonals, the lower boom proper not
+being fixed till the girder having been lifted into place, with the
+diagonal members passing between the cross-girders, allowed this to be
+done. The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being then 2 inches.
+The permanent boom was then put in place, and the girder restored as
+nearly as was practicable to the camber it was intended to have when
+complete, but without throwing, during the process, any improper loads
+upon the old work.
+
+The lower boom being finally riveted up, the cross-girders were made to
+bear upon it by suitable packings. There were, in addition to the new
+girder, two stiff frames between the old main girders, to which the new
+was secured.
+
+The girder was designed with the intention that under dead load only the
+cross-girders should just rest, but throw no weight, upon the new work,
+the latter assisting to carry live load only. The floor beams being of
+small span, and securely riveted to the old girder tops, the centre
+girder was required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion, the three
+points of support of the cross-girders thus not altering their relative
+levels. That this resulted was evident from the fact that, previous to
+connecting the cross-frames to the centre-girder, the work being
+otherwise complete, a space between the two of about 1/2 inch,
+afterwards filled by a packing, showed no alteration, the closest
+measurement failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be expected, very
+marked.
+
+In the conduct of that class of strengthening work which has been dealt
+with in this chapter, it is essential, in the author's judgment, that
+the man responsible for the detailed calculations and design should
+himself see the operations of adjustment carried out, or delegate it
+only to one equally familiar with the requirements.
+
+Before dismissing the subject, it will be well to refer to a method of
+approximately determining flexure curves, of occasional use in dealing
+with centre girder or similar questions. The figure assumed is plotted
+to an exaggerated scale, with which object the actual radius of
+curvature at points along the girder's length are first ascertained by
+the formula
+
+   E � D
+  ------- = R, radius of curvature in feet,
+  _f_ � 2
+
+and the radius of curvature for the diagram by
+
+  12 � R � F� = _r_, radius for plotting, in inches (5)
+
+E being the modulus of elasticity, D the girder's depth in feet, _f_ the
+mean of the extreme flange stresses per square inch of gross area, and F
+the fraction indicating scale as 1/48, where 1/4 inch = 1 foot. The
+curve, being plotted, shows by direct scaling the movement of any point
+relative to its original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn with the help
+of template curves, or even set out as pieces of "straight."
+
+When the curve is laid down so that its chord equals the span to scale,
+the method involves an error of excess in the resulting deflection or
+droop which is as much as 7 per cent. when the mean radius for plotting
+equals the span as drawn, or when the droop of curve approaches
+one-eighth of the span. As the exaggeration of curvature is made less
+pronounced, this error rapidly diminishes, till for a droop of about
+one-sixteenth the percentage is one-fourth part of that above given.
+This excess in the droop of curve may be amended by the following
+expression:--
+
+          (droop�       )
+  droop - (------ � 3�73) = corrected droop, or deflection.
+          (chord�       )
+
+For some purposes it may be preferable to amend the radii for plotting,
+so that the curve, as laid down, shall be correct, which may be
+effected by the formula here given, to be applied to each value of r, as
+first ascertained:--
+
+        (chord�        )
+  _r_ + (------ � �0625) = corrected plotting radius.
+        (  _r_         )
+
+If, however, the length of curve is made equal to the span (the chord
+then being less), and the radii for plotting as given by (5) are used,
+the result will for most purposes be sufficiently precise, though there
+will now be an error of a contrary kind, which, for a curve having a
+droop of one-eighth, will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described by
+Professor Fleeming Jenkin in the article "Bridges" of the "Encyclop�dia
+Britannica," but without corrections.
+
+A careful comparison of results by the above means, with those
+calculated, shows that with good draughtsmanship they may be relied upon
+for considerable accuracy. Equally applicable to girders of varying
+depth and flange stress, they have also a limited use in cases of
+continuity.
+
+[Illustration: FIGS. 77 and 78.]
+
+Figs. 77 and 78 illustrate the deflection and stress diagrams for the
+cross-girders of the bridge supposed to have been strengthened by a
+centre-girder, when under the influence of live load and a centre
+reaction of a definite amount. As a matter of convenience, each radius
+length has been halved, before correction, so that the resulting droop
+of the curve is twice the true amount.
+
+
+
+
+CHAPTER XII.
+
+CAST-IRON BRIDGES.
+
+
+Cast Iron as a material for bridges has of late years fallen into
+disrepute. It is now entirely tabooed by the Board of Trade for railway
+under-bridges, unless of arched construction. This condemnation of cast
+iron followed, and was apparently the result of, an accident which
+occurred to an under-bridge on one of the southern lines, which bridge
+had already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good, inasmuch as it
+led to a thorough overhaul of all railway under-bridges in this country,
+and the renewal of a great number no longer in a condition suited to the
+carriage of heavy or of passenger traffic; yet there is little doubt
+that, in the author's judgment, many excellent cast-iron bridges were
+then removed at considerable cost, to be replaced by others of wrought
+iron or steel, which will not last so long as many of those displaced
+had done, or would still have lasted had they not been dismantled.
+
+The earlier cast-iron bridges were commonly made of cold-blast iron, a
+material of such strength and toughness as to give an extraordinary
+amount of trouble in breaking up the heavier parts, when the time
+arrived to do this, and with which material ordinary hot-blast iron is
+not to be compared for reliability.
+
+[Illustration: FIG. 79.]
+
+As illustrating the very considerable stress to which cast iron may be
+subjected, without of necessity leading to any mishap, two cases may be
+cited. The first, a bridge of 32 feet effective span, carrying two
+lines of way, each pair of rails being supported upon Barlow rails,
+forming the bridge floor, the ends resting upon the bottom flanges of
+inverted [T]-shaped girders, 2 feet 3 inches deep, as shown in Fig. 79.
+
+The extreme fibre stress works out at 2�9 tons per square inch in
+tension, and 5�9 tons per square inch compression, calculated as it
+would be in ordinary office work; but for the actual loads, at a span as
+above, exceeding the clear span by 6 inches only, and without regard to
+the effects of eccentric application of the load. The girders when taken
+out showed upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be too
+strongly condemned, notwithstanding that in this case no ill resulted.
+It is evident that a piece of the lower flange being broken out from
+this cause, as occasionally happens, might so reduce the section as to
+result in complete failure.
+
+[Illustration: FIGS. 80 and 81.]
+
+The second example is that of a small railway under-bridge of two spans,
+continuous over the central pier, each span being 16 feet 6 inches. The
+rails were supported upon longitudinal timbers lying within
+trough-shaped girders, as shown in Figs 80 and 81.
+
+The stress over the pier, in the extreme fibres of the top flange, is
+estimated at 4�7 tons per square inch in tension, but it should be noted
+that the effect of the timber longitudinal and rail has been neglected
+in arriving at this result, which might possibly on this account be
+reduced to near 3 tons per square inch.
+
+The case is noticeable because no evidence of high stress was apparent.
+The author saw nothing to suggest sinking of the central pier, the
+effect of which, within limits, would be to further reduce the stress as
+calculated; but it is quite possible some slight settlement had
+occurred; this, as the spans were so small, would have a sensible
+effect. While too much reliance should not, it is clear, be placed upon
+any estimated result about which there is a lingering doubt, it should
+be remarked that, as it would be necessary the pier should sink 3/16 of
+an inch, for each ton of reduced stress, it is not probable that the
+results quoted are in excess to any material degree; they are, indeed,
+more probably low, as no notice has been taken of impact.
+
+Though cast-iron girders for railway under-bridges are now prohibited in
+this country for new works, there are still uses to which they may be
+applied, and it may be well to insist that girders of this material
+should be fairly loaded, the weight being brought upon them in such a
+way that there shall be no serious secondary stress, such as arises when
+wide flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking down under a
+load fairly applied. Preference is now given to steel or wrought iron
+for columns; while this is often quite justifiable, there remain many
+cases in which nothing better need be desired for this purpose than good
+cast iron, provided only that the column be loaded in a suitable
+manner--i.e., axially, and that the arrangement and details of the
+super-structure are such that there shall be no cross-breaking efforts,
+or rocking of the column due to temperature or other causes; unless,
+indeed, such cross-breaking or rocking is definitely taken into account
+in designing the work. The same care observed in the detailing of
+cast-iron work that is not infrequently taken in the design of
+structures made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with the
+advantage of greater resistance to rust, and a reduced cost in
+maintenance.
+
+Good cast iron is, in fact, when used with discretion, a most excellent
+material, popular predjudice notwithstanding. The oldest metallic bridge
+in this country at the present moment is of that metal.
+
+The one chief respect in which cast iron is at a disadvantage compared
+with wrought iron or steel is that it does not give premonitory warning
+of failure--it remains intact, or it breaks. The indications of
+weakness, which may be read by an experienced inspector of other
+metallic bridges, are in a great measure absent. There is also an
+objection which may exist, but is to be avoided by good design and care
+in the foundry--viz., internal stress due to unequal cooling. In extreme
+cases this may lead to fracture before the work has left the maker's
+hands, but it can only occur by neglect of ordinary precautions.
+
+[Illustration: FIGS. 82 and 83.]
+
+In a case which has already been referred to in the chapter on
+"Deformations," page 80, an outer rib of a cast-iron arch fractured near
+the crown after fifty-four years' use. Owing to the nature of the
+design, and the fact that the near abutment had closed in slightly,
+bringing the linear arch of necessity near the lower edges of the arch
+segment in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces, at the
+upper edge where fracture commenced. The result was very far from
+explaining the occurrence of the break, but an examination of the
+details shown in Figs. 82 and 83 will make it apparent that, in addition
+to the tensile stress, as calculated, there was probably a severe
+initial stress of the same character due to irregular cooling in the
+foundry half a century before. The sum of these stresses, it is
+suggested, placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent either by
+producing a small further settlement of the foundations, of which the
+author saw no evidence, or, as is more probable, the attachment of a
+rope to this rib for the purpose of keeping a barge in position, which
+certainly did occur, gave the arch rib just such an additional strain as
+to result in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The inner ribs
+were of a much less objectionable section.
+
+[Illustration: FIG. 84.]
+
+Cast-iron arches, though still allowed by the Board of Trade rules, are,
+indeed, liable to be seriously affected by settlement, or yielding of
+the abutments, unless hinges at the crown are introduced. As an instance
+of this may be quoted a bridge of some 45 feet span, in which the arches
+were cast in two pieces abutting, and very efficiently bolted together
+at the crown, the springing and vertical abutment member of the
+spandrel being bolted and built solidly into heavy masonry. The arch
+sank at the crown, caused by, or itself the cause of, a movement of the
+abutment, with the result that the lower bolts at the crown joint broke
+away, rupturing the casting, as shown in Fig. 84. The arch must then
+have acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if a proper
+hinge had originally been provided. The break happened to occur so as to
+leave a sufficiently good bearing face at the crown; there was, indeed,
+no tendency for one surface to slide upon another; but in the accidental
+fracture of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.
+
+A second case of very much the same character has also been under the
+author's observation, though in this the ends of the spandrels were not
+built into the brickwork of which the abutments were composed. Other
+instances of fracture either in the arch proper or in the spandrel work,
+have come under notice, though particulars cannot now be adduced; but
+the examples cited are by themselves sufficient to justify the
+conclusion that it is imprudent to construct a cast-iron arch without a
+central pin or its equivalent, unless the abutments, being exceptionally
+well founded, may be relied upon as free from any liability to move. It
+is, however, to be borne in mind that movement in the abutments of a
+small arch of any given absolute amount is more injurious than the same
+amount of movement in the abutments of large arches of similar design,
+so that what may be negligible in the latter case would perhaps be
+destructive in the former.
+
+To the absence of ductility and liability to initial stress must be
+added yet another disadvantage to which cast-iron work is prone--viz.,
+the possibility of concealed defects, blow-holes or cold-shuts; these in
+good foundry practice are not very likely to occur, but, as they are
+possible, cannot be overlooked in considering the suitability of cast
+iron for bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks by way of
+qualification, the author reiterates his opinion that there is still a
+use for cast iron in bridgework.
+
+With respect to the repair of cast-iron bridges, but little is to be
+said; the possibilities in this direction are very limited. Occasionally
+it may be desired to deal with the fracture of some member in the
+spandrel bracing of an arch, when it is commonly sufficient, and even
+preferable, to limit the repair work to confining the fractured parts in
+such a way as to prevent displacement.
+
+Rarely it may happen that an arch fractures as a result of settlement,
+or other movement, when, if it is decided that safety of the structure
+is not imperilled, it will in this case also be preferable to confine
+the parts simply by flitch-plates or other contrivance, with no attempt
+rigidly to make good the break, the consequences of which treatment
+would probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable, though
+something may occasionally be done by the negative process of lightening
+the dead load, or by remodelling the permanent way. Arches may, however,
+be rendered much more reliable by the introduction of suitable bracing
+where this is either wanting or inefficient.
+
+In scheming such additions it is desirable to arrange for as little
+drilling of the old work as is possible; where this cannot be altogether
+avoided, the position of the holes should be carefully chosen with
+regard to the effect they may have upon the strength of the old work.
+
+
+
+
+CHAPTER XIII.
+
+TIMBER BRIDGES.
+
+
+Timber bridges, though probably the most ancient in type, are yet the
+least durable in any particular instance. The perishable nature of the
+material when used for exposed construction renders it peculiarly liable
+to develop defects which quickly put a limit to the life of the
+structure. In addition to decay in the body of the main members--which
+may perhaps be long delayed, so that a simple beam bridge may last for
+many years--there is in more complex designs decay at connections and
+joints, which proves very detrimental to the integrity of the whole.
+Water running upon the surface of a member gravitates to its lower end,
+and, if there be a joint or other connection, settles there, to be
+productive of lasting mischief. From this cause, together with a very
+common deficiency of bearing surface relative to the forces to be met,
+the joints soon develop some movement; working of the structure
+commences under passing loads, its final destruction being then a
+question of time only. Each joint is, in fact, in timber bridge
+construction a source of serious weakness to a degree which has no
+parallel in well-designed metallic bridges.
+
+Wrought-iron straps to confine the ends of raking members, or for other
+uses, are liable to crush into the wood, and bolts are apt to enlarge
+the hole through which they pass. Wood keys, where these are introduced
+to prevent one timber from sliding upon another, are also prone to
+develop cracks in the main members, and fibre crippling from excess of
+stress. All these defects are, however, in timber-work more easily
+defined than efficiently remedied, as it is barely practicable for any
+but the harder woods to ensure, for heavy loads, a sufficiency of
+bearing surfaces.
+
+The most readily detected evidence of deterioration in timber bridges is
+the sag of its bearing members, or trusses, for the simple reason that
+if there is no local trouble at the joints, there will probably be no
+appreciable drop at the centre of the span. The existence of such a
+depression may, however, be caused in rare instances by the spread of
+the supporting piers or abutments, particularly in the case of beams
+trussed by end diagonal rakers and having no tie.
+
+Bridges formed of deep trusses, with the road upon the top, are
+sometimes found to be wanting in lateral bracing, the result of which is
+that the main trusses go out of line, leaning considerably one way or
+the other, being checked only by such rigidity as the joints and
+floor-beam attachments may have, with possibly some assistance from the
+end connections of the span.
+
+The decay of piles where entering the ground or water is, of course, a
+fruitful source of trouble, as also is the sinking of piles, where these
+are insufficient in number, or have not been well driven in the first
+place.
+
+A vital difficulty with timber structures generally is the uncertainty
+that will commonly exist as to how far decay extends in those cases
+where it has started. Timber does not necessarily show upon its surface
+the evidences of internal rotting. Memel timber may, indeed, be
+sometimes found to have become thoroughly unreliable, yet showing no
+sign of this upon its painted surface. By sounding the wood with a
+hammer, or by probing, its condition may commonly be ascertained. In
+cases of doubt, an auger-hole will make it clear as to whether the
+interior be good or otherwise, as to the particular parts tested; but
+only as to those parts, leaving it a matter of guesswork as to the
+remainder.
+
+[Illustration: FIG. 85.]
+
+A railway bridge having many of the defects which have been indicated
+may be quoted as an example. This structure crossed a canal, supported
+upon piles, some of which were in water, others carrying land spans. The
+canal span consisted of four trusses, one under each rail, or nearly so,
+framed in the manner shown in Fig. 85, precise details not, however,
+being now available. The trusses, apart from deflection under live load,
+sagged considerably--in one instance, 4-1/2 inches; one inside truss was
+also leaning towards the centre line of the bridge as much as 3 inches.
+One raker, or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections and joints
+were also in a bad condition. The vertical tie-bolts of the main trusses
+were all slack. The piles generally, many of which were badly decayed,
+had sunk and inclined towards one end of the bridge about 4 inches in 7
+feet of height, the ground being soft and unreliable.
+
+Movement under a passenger train crawling over the bridge was very
+appreciable, but not startling. There had been introduced, from time to
+time, additional timbers and iron ties, with the object of rendering the
+spans more reliable, but leaving it somewhat difficult to determine the
+function of the several members. The bridge was, of course,
+reconstructed.
+
+[Illustration: FIG. 86.]
+
+[Illustration: FIG. 87.]
+
+[Illustration: FIG. 88.]
+
+An instance may here be cited showing how badly distorted a timber
+structure may become without actually falling. The bridge referred to
+consisted of three spans of 29 feet, each span having two trusses,
+between which ran a colliery tramroad, 1-foot 6-inch gauge; the corves
+running upon this, at 4 feet 6 inch centres, weighed, when full, about
+10 cwt. each. The trusses were badly out of shape, the centre span
+having sagged 5-1/2 inches, with one truss of the same span nearly 10
+inches out of line at the centre. This little bridge, of which some
+details are shown in Figs. 86, 87, and 88, had been in use about twenty
+years.
+
+[Illustration: FIG. 89.]
+
+A third case which may be named is that of a road bridge, about 12 feet
+wide, crossing by thirteen spans a shallow river liable to floods. The
+construction was of a simple character, as indicated in Fig. 89, and
+consisted of piles supporting trussed beams, which had sagged in some
+instances over 2-1/2 inches. The bridge had, some years previous to the
+author's inspection, been heavily repaired, many new strut and
+stretching pieces having been introduced, the piles also being
+reinforced or renewed. Five years before, a traction engine, said to
+weigh 5 tons, had passed across the bridge in safety; but the author
+noticed that a coal wagon, which, with the horse, weighed about 50 cwt.,
+when walked slowly over set up much movement. This bridge had been in
+use nearly thirty years, and was very much out of line from end to end.
+
+Though timber bridges cannot at the best be considered durable, yet, by
+attention to certain points in design and construction, their length of
+life may be materially enhanced. Every cut across the grain may be
+considered an element of weakness by exposing the material to quicker
+decay, for which reason the number of ends, or of joints, should be
+reduced to a minimum. An additional reason for reducing the number of
+joints or other connections is the liability of these to develop
+movement, as already stated, the yield of any one joint, being the cause
+of movement in others, which might, but for this, have remained close.
+These considerations lead to the conclusion that fewness of parts is, in
+timber construction, as in structural work generally, an excellent
+principle to observe. Mortising, elaborate scarf joints, recessing, or
+any cutting into the timber which is not essential, should be avoided,
+the simplest forms of connection being preferable, if at all suitable.
+If a step or butt surface is wanted for any member, it is commonly
+better to provide this by a cleat or other added piece, rather than by
+cutting into the timber butted against.
+
+A complicated joint formed in the body of main timbers can only be
+renewed by renewal of the timber itself, whereas by the method indicated
+the joint is readily tightened, or re-made, without involving the main
+member. Bearing surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake of bearing
+surface in the holes, and reduction of any liability to bend under
+cross-stress. In trusses of the form shown in Figs. 85 and 86, it is
+desirable to introduce diagonal members in the middle bay, even though
+it may appear that the stiffness of the main beams is sufficient to
+render this unnecessary as a matter of strength, as without these there
+is apt to be, under rolling load, a slight distortion, leading to
+working of the joints and free entry of moisture. Lateral bracings
+should also, for much the same reasons, be introduced, even though they
+may not appear necessary in the new structure, with joints all close and
+effective.
+
+Projecting ends of timbers should be carried out well beyond the
+requirement of strength or bearing, in order to ensure a liberal margin
+for that decay in the end fibres which commonly develops. Timbers
+resting upon abutments, or running into confined spaces, should be
+arranged for free ventilation and ready drying. Occasionally joints at
+the lower ends of timbers are protected by lead or zinc flashings to
+prevent water running into them, a method which should have some
+protective value. Whatever measures may be adopted, whether in the
+design or execution of timber bridge-work, will, however, be but little
+effective, if the timber itself is not good of its kind, and well
+seasoned.
+
+Creosoting to be useful should be thorough and something more than skin
+deep. The timber itself should be well dried before treatment.
+
+The repair of timber bridges very largely consists in the renewal of
+decaying timbers, where this is practicable, or in adding supplementary
+pieces where the old cannot conveniently be displaced. Joints may be
+tightened up by hard-wood wedges, properly secured to prevent slacking
+back, all bolts being also screwed up tight, perhaps some additional
+being introduced.
+
+Piles standing in water, which have decayed, may be strengthened by
+driving other piles between the old, or on either side, but not of
+necessity opposite to them, and by means of waling timbers bolted to the
+old piles, put in a position to take load, either by the walings resting
+upon their tops, or being bolted to them. Piles decayed where entering
+solid ground may generally be strengthened by bolting on supplementary
+timbers to reach well above and below the decayed part, or by cutting
+out the bad length, introducing a new piece, and fishing the butt-joints
+in a proper manner. But all remedial measures have generally to be
+considered with reference to cost, as compared with the probable
+increase of life of the structure. With a bridge in an advanced state of
+decrepitude, such repairs may prove anything but economical, and at the
+best defer reconstruction but a very moderate length of time.
+
+
+
+
+CHAPTER XIV.
+
+MASONRY BRIDGES.
+
+
+Masonry bridges, in which description it is intended to include
+structures both in stone and brick, are, when well built, amongst the
+most durable and long-suffering of any which come under the care of a
+maintenance engineer; yet when developing the faults peculiar to their
+kind, they may be the occasion of much anxiety, and render necessary
+frequent inspection, or even continuous watching.
+
+Apart from decay of mortar or material, defects may very commonly be
+traced to the foundations, or to earth-slips. Sinking, when uniform, may
+be quite harmless, though possibly inconvenient; irregular sinking of
+piers or abutments is quite a different matter. It is, however,
+remarkable to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and kind which would
+be fatal to the connections of metallic bridgework is endured by bridges
+of stone or brick; not, it may be, without damage, yet with no occasion
+for alarm. The superstructure of metallic bridges may often, however, be
+restored to the true level before the mischief has become serious,
+whereas in the case of masonry arches this is not practicable.
+
+Spreading of the abutments is very seldom the cause of any great injury
+to an arch, though it is common enough to find old and flat arches
+slightly down at the crown; but the contrary case of abutments closing
+in is not very unusual when these are high, or terminate a viaduct over
+a deep valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected; or, if the
+arches are very solid and heavy, the abutment may slide forward at the
+base, with no sensible reduction of the opening.
+
+When a viaduct connects the two ends of a high embankment, it may happen
+that the end piers are not clear of the embankment slope, in which event
+a pier may, should the bank slip, move with it, as to that part not in
+solid ground; with the result, in a bad case, that it is broken across
+and the superstructure imperilled.
+
+[Illustration: FIG. 90.]
+
+A case of abutment movement is illustrated in Fig. 90, which represents
+the end arch of a masonry viaduct, one abutment of which had moved
+forward in the manner already referred to. From the springing upwards
+the arch retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the movement became
+pronounced, heavy timber centering was introduced, with the object of
+preventing any mishap, the damaged portions being ultimately cut out and
+made good. The structure was thirty-five years old.
+
+The practical utility of stop piers in long arched viaducts is, perhaps,
+rather in checking movement of the tops of piers under moving load than
+in arresting actual failure of a series of arches. That the tops of
+piers do move very sensibly need not be doubted. The author has
+attempted to measure this in the case of piers about 60 feet to the
+springing, by means of a theodolite placed below, but has reached no
+more definite result than that a movement existed, of which he was not
+able to determine the amount. If in a viaduct some arches are more
+heavily loaded than others, each spreading slightly, the end piers of
+the group will move amounts which together equal the sum of the
+individual span spreads, with a tendency in the arches beyond those of
+the group overloaded to rise.
+
+This rocking may be detrimental both to the piers and arches, and helps
+to account for the disintegration of mortar in arches and piers, which
+not infrequently happens. The soffits will sometimes be seen with a
+thick incrustation of lime, which has washed out of the joints, or from
+limestone ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that pieces of stone
+or brick will drop out, necessitating repair at heavy expense, of which
+scaffolding is commonly a large part.
+
+Tall piers may be found badly out of the upright due to sinking of
+foundations. A marked case of this kind came under the author's
+notice--a viaduct of fifteen semicircular arches, in which, though many
+piers were wanting in truth, one in particular was about 1 foot 4 inches
+out of vertical, making one side of the shaft plumb, and doubling the
+normal batter of the other. Inquiry showed that in this instance the
+pier had never been upright from its earliest history dating back
+thirty-six years. This makes clear the desirability, to avoid hasty
+conclusions, of ascertaining, when it is possible to do so, the complete
+record of any structure.
+
+A bridge fifty-eight years old, of three skew spans, carrying a railway
+over a canal, and having somewhat flat brick arches with stone quoins
+upon low piers, developed the somewhat unusual defect, as to the centre
+arch, of splitting along its length for about 10 feet, parallel to and
+some 7 feet from one face. In this case there was reason to believe that
+there had been considerable local settlement of the piers on that side
+of the bridge. The arches were otherwise in bad condition, the brickwork
+poor, and the mortar decayed. Each arch was down at the centre, and
+displayed a fault not unusual where bad brickwork joins up to good cut
+stonework, the quoins showing a tendency to separate from the brick
+rings. Below the bridge were coal-workings.
+
+Brick arches built in parallel rings sometimes separate one ring from
+the other, demonstrating the known propriety of bonding the rings
+together properly, and of carrying the arch round, when building, at its
+full thickness.
+
+[Illustration: FIG. 91.]
+
+An instance of bridge failure from a somewhat peculiar cause may be
+quoted as of some interest, largely because the structure was very
+ancient, having been in existence some 400 years. This bridge, carrying
+a road, was of the type usual in old masonry bridges over a river,
+having small arches, thick piers, and solid backings to the arches. Two
+flood-openings at one end had, by sinking and want of care, become
+partly closed. The centre arch had, however, been widened about 140
+years previously. During a severe flood, the swollen river, overflowing
+its banks, trespassed upon a timber yard a little above bridge, and
+washed down into the stream a large quantity of sawn timber; this,
+unable to get through the main arch with freedom, compacted into a
+serious obstruction. The flood water, thus checked in its passage, seems
+to have scoured below the timber, and robbed the piers of such support
+as they formerly had (see Fig. 91). The bridge stood in this condition
+till the water lowered, when the middle part of the structure broke up,
+and subsided into the hole which had been washed out. But for the
+monolithic character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers stood had
+been partly undermined for very many years. The case is instructive, as
+showing how a slight accident--powerless by itself to work mischief--may
+be very damaging when allied with so powerful an agent as running water.
+
+[Illustration: FIG. 92.]
+
+The enduring character of even the roughest class of masonry arch, if
+only the material be good and abutments stable, is shown when it becomes
+necessary to destroy old work of this character. Fig. 92 represents a
+short length of "cut and cover" arching in process of demolition, just
+before it fell in. The masonry was of hard sandstone rubble and had been
+cut away, as shown, till at the point A only a very small piece of the
+arch remained, when the length finally broke up and dropped. Arches have
+commonly a great reserve of strength; tunnel linings are, indeed, often
+badly out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed or bulged,
+to serve the purpose intended.
+
+Though the equilibrium of masonry arches has been the occasion of much
+profound study, and the nicest calculation has sometimes been applied to
+the design of such work, yet it appears that when an arch is well backed
+up, the theoretical linear arch need have but little connection with the
+figure of the intrados; a statement consonant both with common-sense and
+the teachings of experience. With solid backing, this would indeed seem
+to be more important than any part of the arch ring below the top of the
+backing, the lower part of the ring serving chiefly to preserve the face
+of the solid work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure would seem to
+be inevitable. The masonry or brickwork does not always show evidence of
+damage, if the distortion has been slow; suggesting that structures of
+this kind have a power of accommodation with which they are not
+generally credited.
+
+A noticeable cause of deterioration of masonry structures, which may be
+quite independent of settlement, is serious vibration. This is well
+known in connection with church belfries, and is also locally apparent
+when telegraph or other poles are attached to masonry parapets.
+Vibration, when caused by heavy railway traffic, acting upon arches
+light or originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially built, and
+particularly those carrying ordinary roads, and not subject to much
+vibration, have great lasting powers, if repaired with skill, or even
+let alone. Distortion of the arch may be quite consistent with practical
+stability, if the movement or decay with which it originated is not
+progressive, or has been arrested. In this connection a distinction is
+to be made between arches well backed, to which the foregoing remarks
+apply, and in which the two halves of each arch may act as separate
+monoliths meeting at the crown, and the case of a true arch ring
+independent of any outside resistance, such as backing or spandrels may
+give, and depending almost wholly upon the proper balance of its
+component voussoirs for its stability. With the latter class of
+structure no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way, and the work
+is dealt with judiciously, if at all. It must, however, be understood
+that there are limits as to what may be done effectively, short of
+rebuilding, in dealing with structures in which, perhaps, brickwork is
+rotten and mortar decayed and crumbling, the whole being little better
+than a broken mass of rubbish.
+
+In cases where it may be prudent to introduce safety centring, as in an
+instance already referred to, it is commonly expedient to refrain from
+causing this to take any sensible part of the load till all movement has
+ceased, the centres being at the outset largely precautionary. The
+requirement with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement is still going
+on, the effect may be to cause the arch to break up upon the centring,
+and precipitate repair work which might otherwise have been left to a
+more convenient time, when all movement had stopped or been checked by
+suitable measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt with
+piecemeal by cutting out the bad places, a small part at a time, and
+making good. The work requires the greatest care of experienced men.
+
+Pointing masonry or brickwork is effective for little other than
+protective purposes, and to check further weathering; it has obviously
+no effect upon the interior work, and if made to cover up the evidences
+of internal decay, is even misleading and objectionable. In extreme
+cases it may be desirable to open out the road and deal with the
+filling, to relieve or to strengthen the outer spandrel walls, which
+sometimes bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise repairing solid backing,
+in which operations some regard must be had to the effect of the work
+upon the balance of the opposing halves of the arch.
+
+Of the different classes of masonry commonly used in bridgework, it may
+be well to remark that good coursed rubble, or preferably that variety
+bonding both vertically and horizontally, of a durable stone, perhaps
+quite unfit for any but rough dressing, may make a most lasting
+structure, the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from the block,
+probably along some line of relative weakness--there is no "nursing" of
+weak corners; whereas with stones reduced to a perfectly regular shape
+by chisel work, the plane surfaces and geometrical angles are made with
+partial regard only to the natural grain of the stone.
+
+
+
+
+CHAPTER XV.
+
+LIFE OF BRIDGES--RELATIVE MERITS.
+
+
+The life of bridges of differing materials has been incidentally touched
+upon by the examples quoted, in dealing with each class of structure. It
+will be useful to recapitulate some of the facts adduced, and to compare
+the terms of life so far as they appear to be indicated; but in doing
+this it is necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history. The
+duration of any such structure may be limited by adverse conditions,
+peculiar to the case considered, by defects of design, material, or
+workmanship--present from the first--or by neglect, overloading, or
+accident, making up its later record.
+
+With the exception of timber structures, it is difficult to find any
+class of bridges furnishing examples which have reached the limit of
+life, independently of the evils named, and as a result of unavoidable
+decrepitude. There are none the less influences at work tending to this
+condition, and which it is too much to expect can in all cases be
+foreseen or completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and minor
+faults in design, which even in the most capable hands may be expected
+ever to fall short of perfection. At the best, then, the life of any
+structure, though long, must have a limit. With bridges of more average
+or inferior qualities the life may be positively short, even without the
+destructive influence of overloading.
+
+Dealing with instances of metallic bridges, the adjacent table gives the
+time each had been in existence when removed, and some indication of the
+reason for its condemnation. Those marked with an asterisk were cases of
+pronounced high stress. From a study of the table it appears that in
+actual practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and thirty-six
+years; but these figures applied to this collection of cases only. It is
+to be remarked that many other bridges outlasted these, and are likely
+to continue reliable. These results show, then, no more than that some
+wrought-iron bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as indicating that
+the durability of such structures is by no means so limited as the table
+would suggest. It is to be observed that, as design and maintenance are
+now better and more generally understood than when experience was
+largely wanting, it is to be expected that later examples will show no
+such poor results.
+
+Of steel bridges little can be said, because of the limited time this
+material has been in use; but the generally acknowledged belief, quite
+in agreement with the author's observation, that steel rusts more freely
+than wrought iron, suggests that such bridges will have a shorter lease
+of life, the more so that the surface-to-section ratio is also greater
+for higher unit stresses, though other adverse influences are much the
+same for one material as for the other.
+
+Of cast-iron structures but few cases have been given; of these,
+cast-iron arches have been noticed as developing defects which led to
+reconstruction, or to limiting the loads to be carried. Plain cast-iron
+girders, on the other hand, have never, under the author's direct
+observation, been removed for any other reason than because they were
+cast iron, or from over-stress, due to the growth of loads; never from
+defects or wasting, though it is not suggested no such cases exist. The
+author has no evidence which points to what may be the limit of life of
+a good cast-iron girder fairly treated.
+
+_Examples of Life of Metallic Bridges._
+
+  -------------------------+-------+------+----------------+------------
+        Description.       | Span. | Age. |   Defect.      | Reference.
+  -------------------------+-------+------+----------------+------------
+                           |ft. in.|Years.|                |
+                           |       |      |                |
+                                _Wrought Iron._
+                           |       |      |                |
+  Plate girders            |  (?)  |  12  |Loose rivets    |
+    *Ditto                 | 35  0 |  12  |Ditto           |p. 52
+     Ditto                 | 55  0 |  14  |Rust. Distortion|pp. 78 & 97
+  Trough girders           | 11  0 |  16  |Loose rivets.   |p. 50
+                           |       |      |Cracked webs    |
+  Plate girders            |  (?)  |  22  |Loose rivets    |
+  Twin girders             | 31  6 |  23  |Weak. Cracked   |p. 13
+                           |       |      |webs            |
+     Ditto                 | 35  6 |  23  |Weak. Distorted.|p. 74
+  Plate girders            | 42  0 |  23  |Loose rivets.   |p. 21
+                           |       |      |Cracked webs    |
+     Ditto                 | 72  0 |  29  |Weak. Loose     |p. 53
+                           |       |      |rivets          |
+     Ditto                 | 47  0 |  24  |Distortion      |p. 9
+     Ditto                 | 32  0 |  32  |Rust. Cracked   |p. 14
+                           |       |      |webs            |
+    *Ditto                 | 25  0 |  36  |Weak            |p. 63
+                           |       |      |                |
+                                  _Steel._
+                           |       |      |                |
+  *Trough girders          | 15  8 |  32  |Weak. Rusted    |pp. 68 & 98
+                           |       |      |                |
+                                _Cast Iron._
+                           |       |      |                |
+  *Girders                 | 32  0 |  36  |Weak            |p. 141
+   Girders, cast-iron piles|  (?)  |  44  |Ditto           |
+   Arches                  | 45  0 |  55  |Crack. Settle-  |p. 145
+                           |       |      |ment            |
+     Ditto                 |100  0 |  62  |Crack. Deforma- |pp. 80 & 145
+                           |       |      |tion            |
+  -------------------------+-------+------+----------------+------------
+
+With timber bridges the length of life appears to be about twenty-five
+years, but this is very largely dependent upon the question of
+maintenance, and may range from fifteen to thirty-five years. It is
+manifest that repairs, when extensive and consisting of the renewal of
+the more essential parts of the structure, border upon reconstruction,
+and may be continued indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for railway
+bridges, be taken as stated, though for highway bridges possibly longer.
+
+Of masonry bridges little is to be said but that it is only in cases of
+bad work or material--with, perhaps, vibration or settlement--that these
+have a shortness of life comparable with that of defective metallic
+bridges. Where these adverse conditions obtain, heavy repairs may be
+necessary before the structure is many years old; but, under reasonably
+fair conditions, bridges of masonry may be expected to outlast
+structures in any other material. Apart from road-bridges which are
+admittedly long-lived, there are a large number of railway bridges and
+viaducts of masonry which, despite heavy loads and vibration, have been
+in use for the past seventy years.
+
+Dealing with the cost of maintenance, this with bridges of wrought iron
+or steel should result simply from scraping and painting, with such
+other incidental work as may be necessary on the subsidiary materials
+used in the structure. The cost of painting will vary with the height
+and character of the bridge, and the amount of scaffolding, if any, and
+may be from 5_d_. to 1_s_. or more per square yard; this if distributed
+over five years, a not unusual interval between each painting, works out
+at an appreciable figure, which may vary from one-third to one per cent.
+of the first cost, per annum. The yearly cost of painting steel-work
+will, for shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be necessary,
+repairs and possibly strengthening, which may raise the total cost of
+maintenance very considerably.
+
+Cast-iron bridges, being less liable to rust, cost less for painting
+than other metallic bridges; and if the cast iron is closed in by
+masonry, practically nothing; they do, indeed, involve very little
+expenditure in the maintenance. Not being very amenable to repair or
+strengthening, cast-iron bridges commonly remain very much as built, or
+are reconstructed.
+
+The proper care of timber bridges may become costly as the structure
+gains in age, and soon grow to a very wasteful expenditure. This is
+evident when it is considered that repairs may be necessary after ten
+years, and that whatever may have been the cost of any part when new, it
+cannot be replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions to be
+observed in dealing with an old structure carrying its load. In addition
+to ordinary repairs, there will be paint or other protective coating to
+be applied, though this is not always done.
+
+The upkeep charges of masonry bridges will be practically nothing in
+favourable cases; but, on the other hand, where extensive repairs become
+necessary, may reach a considerable amount. Exceptional outlays are,
+however, infrequent, and may be spread over a large number of years, in
+those rare instances in which they become imperative.
+
+  _Durability._      _Maintenance     _First Cost._
+                     Charges._
+
+  Masonry            Masonry          Timber
+  Cast Iron          Cast iron        Masonry
+  Wrought iron       Wrought iron     Steel
+  Steel              Steel            Cast iron
+  Timber             Timber           Wrought iron
+
+For purposes of ready comparison, placing bridges of the materials under
+review in order of durability, they would appear as in column 1 of the
+table above; in order of low maintenance charges, generally as in column
+2; and in order of low first cost, as in column 3. With respect to the
+question of first cost, the arrangement of the third column applies only
+to small bridges, say, up to 70-foot span; and, being liable to
+variation with the conditions, is but approximately correct. The less
+costly descriptions of masonry are alone considered in this connection.
+
+It may be added that the total yearly charge of interest on first cost,
+redemption, and maintenance, appears to be for masonry bridges, about
+one-half only of the corresponding totals for bridges of wrought iron,
+steel, or timber; those of cast iron taking an intermediate place.
+
+Summarising the above considerations, and dealing with the relative
+merits of bridges in the different materials, it may be broadly stated
+that for conditions at all suitable nothing seems to be superior to
+masonry--including in this description first-class brickwork--whether
+for road or railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little affected by
+increase of loads. The mass of a masonry arched structure is so great,
+and the margin of strength commonly so liberal, that considerable
+increments of load may have but little effect upon the reliability of
+the structure.
+
+Cast iron has, for bridges of simple design, a strong claim to the
+second place, though its want of ductility is a demerit. It can,
+however, have but a limited use in bridge construction, being applicable
+only to small girder spans and skilfully-designed arched structures.
+
+For bridges of moderate span in which the question of cost does not
+control the matter, wrought iron should probably come next, steel being
+best reserved for those of a larger size, in which weight of the
+structure greatly affects economy.
+
+Timber may be regarded as a material rarely to be used in this country
+for structures to occupy a permanent place, unless for urgent economic
+reasons of the moment.
+
+While expressing this general view of the matter, it is to be admitted
+that the propriety of these conclusions is somewhat discounted by the
+difficulty there now is in obtaining cast iron of the desired
+toughness, or wrought iron with promptitude and sufficient variety of
+section at a reasonable price.
+
+It is apparent, also, that the choice of material may be largely
+influenced--even determined--by considerations of headway, construction
+depth, or character of foundations; so that no very definite rules can
+be usefully laid down, though the adoption of unsuitable materials has
+not been so unusual as to make these suggestions altogether
+purposeless.
+
+
+
+
+CHAPTER XVI.
+
+RECONSTRUCTION AND WIDENING--CONCLUSION.
+
+
+The need for the reconstruction of bridges, arising from various causes
+which have been treated in the preceding chapters, original weakness or
+faults in design, decay or defects, may also be caused by such
+extraneous considerations as the growth of loads, widening of the
+openings spanned, or improvement of the headway.
+
+In any case, a precise survey or measuring up of the structure and its
+immediate surroundings is required, in the execution of which the
+greatest care is desirable, and with respect to which it may be well to
+give a few hints.
+
+The surveying chain, when used, should be tested, the measure of
+accuracy required rendering this imperative in a degree peculiar to work
+of this class. Linen tapes should also be compared with a reliable steel
+tape, and used only where sufficiently accurate for the particular
+purpose. A careful and observant man may do very good work with a linen
+tape, making just that allowance in the sag of the tape which corrects
+for the inevitable stretch; but there is still some uncertainty involved
+in its use, and the author prefers to rely upon a steel tape,
+notwithstanding the inconvenience commonly experienced from its
+intractable nature and liability to damage.
+
+Instruments used must also be in the best adjustment; as errors, which
+in ordinary field work may not be of great importance, are inadmissible
+in bridge work.
+
+It is not necessary here to enter upon the methods of small survey
+work, but it may be desirable to point out that abutment walls should be
+plumbed for verticality; girders, which are liable to be leaning,
+defined in position by reference to their bearings; and generally that
+it should never be taken for granted that there is truth in old work, or
+that this may be assumed as to line or level.
+
+In cases where disputes with any local authority as to headway are
+likely to arise, it is prudent to supplement the information as to level
+of soffits by rods cut to length in strict agreement with the clear
+height, before removing the old superstructure.
+
+It is apparent that in cases where the superstructure is already
+condemned, the detail measurements may be confined to that part of the
+structure which is to remain, securing only such information as to the
+work superseded which may be required in arranging for the new work.
+
+In taking particulars of skew bridges, needless as the warning may seem,
+it is yet necessary to remark that there may be right or left-hand skews
+which will not reverse. The author has known a disregard of this to make
+serious trouble in two instances.
+
+Dealing first with reconstruction of the superstructure of railway
+under-bridges, these, if small, may not give much trouble, though the
+demand for greater strength will, perhaps, involve some difficulty in
+working to the limiting construction depth--i.e., the distance from the
+top of rail to soffit of bridge--particularly as many old bridges have a
+very niggardly allowance in this respect. It may be, and quite commonly
+is, necessary to raise the rails a small amount, or, if headway is not
+restricted, to lower the soffit. Clearances between the running gauge
+and girder-work may also be difficult to secure, more liberal allowances
+being now required than formerly. Complications in the character of the
+permanent way, so frequently found upon old bridges, should, of course,
+be got rid of, if possible; but the endeavour may introduce further
+difficulties. Regard must throughout be had to the methods to be adopted
+in removing old work and in erecting the new. Perhaps the simplest case
+to deal with is that where girders lie parallel to, and under the rails,
+with a timber floor upon which the permanent way is carried, as sections
+of the road involving pairs of girders may be readily removed, and
+replaced by the new girder-work (see Fig. 93). If the deck be of trough
+flooring or old rails, the matter may not be so simple, as regard must
+then be had to the position of joints in the existing floor, and the new
+work be schemed with respect to the number and office of girders which
+may be got in at any one breaking of the road. A slight slewing of rails
+may sometimes be resorted to on occasion, where this has the effect of
+releasing some part of the work not otherwise to be dealt with.
+
+[Illustration: FIGS. 93 and 94.]
+
+Bridges having main girders, with timber or trough flooring resting upon
+the bottom flanges, or suspended by bolts, will, if carrying many roads,
+cause some little difficulty, as the dismantling of any one span
+involves the disturbance of others; where, however, many lines are
+concerned, it may be feasible to put one or more temporarily out of use,
+preserving the continuity of traffic over those which remain, but
+refraining from any diversion of the more important roads.
+
+Somewhat similar troubles occur where main girders with cross-girders at
+the lower flanges are found, particularly if the cross-girders are
+arranged in line, the ends abutting on each side of the same main girder
+webs. It is seldom, however, that this construction is used in bridges
+of small span carrying many roads; but where it does occur, it may
+necessitate the use of timbering below, to carry the ends of
+cross-girders when freed from their supporting main girders. (See Fig.
+94.)
+
+[Illustration: FIG. 95.]
+
+If it is proposed to use new main and cross-girders, it is desirable to
+arrange these in the manner already recommended, the cross-girders not
+in line; this has peculiar advantages in reconstruction work, as the
+bolting up and riveting of the cross-girder ends is not hampered by
+other cross-girder attachments, leaving each piece of floor complete in
+itself. Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence of
+one span from those adjoining (see Fig. 95); but the method is wasteful
+of space, and involves a somewhat greater total weight in the main
+girders.
+
+The foregoing observations apply more generally to small single-span
+bridges, the operations on which may be effected without any material
+disturbance of traffic arrangements; though this can seldom be wholly
+avoided, it should be confined, where practicable, to a few hours on a
+Sunday.
+
+The reconstruction of bridges over 70-feet span may have to be dealt
+with under more elaborate arrangements, if carrying two lines only,
+possibly with single-line working for a period more or less protracted;
+or it may be necessary, having regard to the weight of main girders to
+be removed, to carry the whole structure upon temporary staging,
+supporting the road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed erection in
+its ultimate position, or by erection at one side and drawing across.
+The latter method is, however, commonly reserved for cases in which no
+special staging is used under the old structure.
+
+Bridges of a number of openings are usually dealt with by securing full
+possession of one road at a time, which for double-line bridges
+necessitates single-line working. It is commonly out of the question,
+even with moderate spans, to deal with some of these only at a time, and
+so avoid continuous possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new main
+girders do not in any way interfere with those of the old, and where it
+is not necessary to reset bed-stones, or make other alterations in the
+bearings which necessitate the complete clearance of the pier-tops. In
+exceptional cases it may be found possible to arrange for the complete
+removal of a small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.
+
+Spans erected to one side of the final position, to be later travelled
+across, are commonly mounted upon gantry staging, and up to 50 tons
+weight may rest directly upon rails well greased. The power adopted to
+move the span is usually that of screw or hydraulic jacks, or
+occasionally engine haulage, special tackle being in that case necessary
+to apply the engine power in the right direction. If the time is
+limited, or weight considerable, a more elaborate arrangement by which
+the load is supported upon wheels, may be necessary, with a view to
+reducing the resistance to a manageable amount. All work which it is
+possible to do before shifting into place, including the permanent way,
+where this is of a special character, should be executed in advance,
+leaving only the rail connections to be made good when the span is in
+position.
+
+Where timber staging is used to carry the permanent way before
+dismantling an old structure, it is convenient to begin by placing stout
+balks of timber under the sleepers from end to end of the bridge, or
+directly under the rails if space is limited; the staging is then
+arranged to give support to the running timbers.
+
+Metallic under-bridges of ample headway, perhaps over coal-workings
+(since settled down), or for some less sufficient reason made of metal,
+may be cheaply replaced by brick arches built below the old
+superstructure, the springings of the arch being checked into the face
+of the existing abutments. With stout walls, careful work and good
+material will make this an efficient and durable job.
+
+It being a primary condition of reconstruction work to interfere but
+little with ordinary traffic arrangements, single-line working is
+avoided wherever practicable; as this, always objectionable, may
+necessitate the erection of special signals and signal apparatus,
+besides the temporary remodelling of the roads, and in this country may
+involve also a Board of Trade inspection--altogether a troublesome and
+expensive business.
+
+Any bridgework which is accompanied by breaking or blocking the road can
+only be undertaken by arrangement with the traffic department, after
+notice duly given and published in the periodical record of such
+matters; it is generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand as is
+possible. Wherever practicable and prudent, the whole work is released
+from its surroundings, masonry cut away, rivets cut out and replaced by
+good bolts, nuts removed from holding down bolts, or the bolts cut
+through, etc. Particular care should be exercised to ascertain what
+remains to be done immediately prior to removal. It is necessary further
+to arrange for trucks to be in readiness to receive old material, and
+others containing new girder work to be conveniently stationed, having
+been loaded up to come right end foremost; engine power, cranes, empty
+and loaded trucks, being all marshalled and so placed as to be available
+in proper order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or as to the
+reach of the crane in effecting its work.
+
+The whole operation to be conducted on any Sunday should be well within
+the resources of the men and plant engaged in it, or so managed that it
+is a matter of no serious importance if the whole cannot be completed as
+originally desired.
+
+Possession of the roads to be blocked having been secured between
+certain hours, if some part only of the work to be carried out has been
+completed as the time grows short, any attempt to execute the remainder
+may result in checking trains until such time as the line may be
+reported clear--a contingency to be avoided--though the temptation to
+save another Sunday's work by delay of a few minutes to some one train
+may be considerable.
+
+In scheming any reconstruction, it may be insisted that at least one
+feasible method of carrying out the work must be secured, though it is
+the author's experience that frequently some other method than that
+contemplated is in the end adopted, when, some months later, the final
+arrangements for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered, with a view
+to a moderate amount of work being done at any one time, and to achieve
+as much more as he can himself secure by scheming, or a liberal use of
+labour; all Sunday work, with attendance of engines and cranes, being of
+necessity expensive.
+
+Railway over-bridges do not commonly present any particular
+difficulties. The spans to be dealt with are usually small, and the
+weights to be lifted moderate. The height above rails may, however, be
+above the lift of any crane; and, for the purpose of raising main
+girders, a derrick may become necessary, the rearing and guying of which
+may block many roads during the time it is in use. The girders of larger
+spans, too unmanageable to be lifted whole, may be erected upon staging;
+to secure the requisite headway it may be necessary to build the girders
+at a level above that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the staging.
+
+The widening of railway under-bridges is, as a rule, a matter of no
+special difficulty, but some remarks may be of use. Widenings should be
+planned with a regard to later reconstruction of the original bridge, if
+that is at all likely to be necessary, and with the object that, when
+complete, the whole should be a consistent piece of work.
+
+It may, indeed, happen that widening of a bridge may involve the
+remodelling or reconstruction of the old work, to enable the new roads
+to be laid down as desired; this is more likely to be necessary where
+there exist main girders not competent to take any additional load, and
+to duplicate which would sacrifice space between the new and old roads;
+or it may be unavoidable because of slewing of the old rails, as part of
+a general rearrangement.
+
+[Illustration: FIG. 96.]
+
+Dealing with widenings simply, there is often some little trouble in
+contriving a connection between the new and the old work, as this may
+have to be made under, or close to, the sleeper ends of the existing
+roads. It is desirable to arrange this part so that no drilling of old
+work for rivets or bolts shall be necessary, there being, in fact, no
+strict connection. By judicious scheming, this may be effected, whilst
+securing freedom from leakage of water at the joint. (See Figs. 96 and
+97.) If tying of the new and old structure is desired, this can usually
+be done quite simply, well below the floor at some more accessible
+level.
+
+[Illustration: FIGS. 97 and 98.]
+
+The strict jointing-up of trough flooring, new to old, at right angles
+to the troughs, cannot be contemplated, but may be dealt with by
+treating each part independently, the ends being near together,
+separated by the space of an inch or so. Each trough end being closed up
+by a diaphragm or oak block to prevent ballast dropping through, the top
+of the space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions to
+take away leakage, as it is practically impossible to make this
+arrangement "drop dry" under the conditions common in executing work of
+this kind (see Fig. 98).
+
+[Illustration: FIGS. 99 and 100.]
+
+Where trough flooring, new and old, has to be made good parallel to the
+troughs, the difficulty of making a direct connection is less marked,
+and it is not unusual to introduce a strip cover simply; but if
+accessible, the work is still troublesome, as there is commonly a want
+of strict alignment and truth as to level, between the new and the old
+troughs. It is preferable to arrange for junctions of a more convenient
+type, as in Figs. 99 and 100.
+
+When widening masonry arch bridges by girder-work, it is desirable to
+insure that any girders parallel to the masonry face shall be
+sufficiently far removed from it to enable painting to be executed. The
+space remaining between the girder and the arch may then be bridged by
+floor-plates, or an extension of the timber floor if that is adopted.
+
+In effecting a junction such as this, the author has used the
+arrangement shown in Fig. 101, the advantage being that the piece of
+connecting-floor is sufficiently wide, and also sufficiently flexible,
+to allow the girder-work freedom to deflect without doing harm. The load
+carried by the width of floor is, as to one part, delivered well on to
+the old masonry, in preference to being imposed near to the face. If it
+should for any reason be imperative to place the girder close to the
+arch face, it is preferable to scheme the floor so that there shall be
+no actual contact, the new floor in that case slightly overhanging the
+masonry, as in Fig. 102, or dealt with as in Fig. 103, if depth is
+restricted.
+
+The widening of masonry arch bridges by masonry, calls for no other
+remark than that the new work should be free from the old; though it may
+be advisable, when the widening is narrow, to tie the new work to the
+old in such a way as to permit independent settlement.
+
+If the widening is exceptionally narrow, there may be no choice but to
+bond the new and old work together, and in the best manner, with the
+object of minimising the risk of separation.
+
+[Illustration: FIGS. 101 and 102.]
+
+[Illustration: FIG. 103.]
+
+The above matters relative to widenings, though apparently trifling, may
+by neglect cause much trouble and expense in maintenance. They
+principally concern small bridges, the extension of larger structures
+coming rather in the category of independent works.
+
+
+CONCLUSION.
+
+In bringing these chapters, dealing largely with questions affecting
+maintenance, to a close, it may be well to draw attention to the fact
+that economy in design (apart from improper reduction of sections) goes
+hand-in-hand with economy of upkeep. Given good material, that which
+favours low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to girders,
+favours also small expenditure in maintenance. The less complex the
+design, the easier will it be to keep the structure in order; the less
+the number of parts, the fewer will be the connections. Freedom from
+smithing eliminates liability to failure at cranks, or other work which
+has been subject to fire. It is apparent also that the free use of
+rolled instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A liberal depth
+to all girders, by reducing deflections, limits the inclination of the
+ends and gives the connections a better chance of remaining intact.
+Lastly, with work of this character, the labour of scraping and painting
+is simplified and cheapened.
+
+The author wishes to reiterate the statement made in the opening
+paragraphs of this book, that all instances of decrepitude, failure, or
+peculiar behaviour cited, have been under his direct observation. The
+fact is insisted upon simply that the reader may appreciate that the
+information is at first hand.
+
+It has not been thought necessary, nor was it considered desirable, to
+indicate the locality of each case referred to; but it may be said that
+the matter of these chapters has been accumulating during many years,
+and relates to structures under the control of many different bodies.
+
+The study of old bridges is strongly recommended, particularly with
+respect to stress and strain, which in structures new or old, occur
+possibly as may be expected--certainly as they must. Consideration of
+existing work may thus be a useful check upon the fanciful requirements
+of some methods of design. There is a recent tendency, for instance, in
+English practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many old bridges
+carrying their loads with no sign of distress, should have failed long
+ago. Excess in riveting is a common extravagance, to which the same
+criticism may in a less degree apply. Considerable impact allowances for
+girders of large span may also be referred to as an application of
+empiric theory not justified by experience, which, as in all cases where
+such considerations fight with facts, should be modified or rejected.
+
+
+
+
+INDEX
+
+
+  Abutments, leaning, 82, 173
+  -- movements of, 158
+  -- settlement of, 78
+  Adjustment of centre girders, 128
+  -- of distributing girders, 120
+  Angular distortions, 88
+  Arches, equilibrium of, 162
+  -- repair of, 163
+  Arrangement of cross girders, 21, 175
+  Asphalt, 26
+
+  Ballast, 29
+  Bearing pressure on rivets, 47, 51, 57
+  Bearings, skew, 4
+  Bottom booms, end bays, 18
+  Bracing, additional, 117
+  -- effects of, 34
+  -- flat bars, 37
+  -- incomplete, 41
+  -- sea piers, 42
+  Bridge floors, 20
+  -- repairs, 107
+  -- surveys, 107
+  Bridges, life of, 165
+  Breaks in [T] bars, 16
+  Buckling of webs, 16
+
+  Camber, 24, 80
+  Cast-iron arches, 80, 145
+  -- -- bridges, 141
+  -- -- columns, 7,144
+  -- -- girders, 141
+  -- -- in sea water, 101
+  Centre girders, 122
+  Cinder ballast, 29
+  Cold-blast iron, 141
+  Cooling stresses in cast iron, 145
+  Construction depth, 173
+  Corrugated sheeting, 29
+  Cost of centre girders, 135
+  -- of maintenance, 168
+  Counterbracing, 19
+  Cracked bedstones, 3
+  -- columns, 7
+  -- web plates, 13, 14, 15, 50
+  Cross girder arrangement, 21
+  -- girders, fixed ends, 22, 118
+  -- -- rusted, 29, 97
+  -- -- weak, 30, 66
+
+  Decay and painting, 96
+  -- of floor plates, 109
+  -- of timber, 28, 150
+  Deflection, 85
+  -- due to booms and web, 86
+  -- exceptional cases, 88
+  -- in new and old work, 85
+  -- working formul�, 87
+  Deformations, 73
+  Depth of girders, 23, 89, 184
+  Diagonal ties, 19, 42
+  Distortion due to temperature changes, 79, 84
+  Distributing girders, 120
+  Drainage holes, 25
+  "Drop" loads, 89
+  Dwarf walls under floors, 26
+
+  Early steel girders, 68
+  Economy, 184
+  Effect of earth slips, 157
+  -- of floor on deflection, 88
+  -- -- -- on stresses, 23, 30
+  -- of high stress, 86
+  -- of permanent way on stresses, 18
+  --of skew on bridge floors, 25
+  -- -- -- on centre girders, 131
+  -- of transverse bracings, 34
+  -- of vibration on masonry, 162
+  -- of wave action on sea piers, 42
+  End bays, bottom booms, 18
+  Equilibrium of masonry arches, 162
+  Examination of bridges, 107
+  Examples of cast-iron bridges overstressed, 141
+  -- of high stress, 70
+  -- of life of bridges, 167
+  -- of rivet stress, 56
+  -- of strengthening, 114
+  -- -- -- by centre girders, 131, 134
+  Excessive bearing pressure, 51
+
+  Faulty workmanship, 80
+  Fixed ends to cross girders, 22, 118
+  Flange stresses, 63, 66, 67
+  Flanges, side loaded, 9, 73
+  Flat bar bracing, 37
+  Flexing of girders, 9, 74, 76
+  Flexure curves, 138
+  Fractured bedstones, 3
+  -- rails, 30
+  -- webs, 13, 14, 15, 50
+  Fractures in cast iron, 7, 145
+
+  Girder bearings, 2
+  Girders on columns, 7
+  -- on masonry, 8
+  Girderwork in masonry, 101
+
+  Headway, 173
+  High stress, 61
+  -- in cast iron, 141
+  -- in rivets, 47, 52
+  Holes for drainage, 25
+
+  Impact, 20, 62
+  Inclination of girder ends, 23, 53
+  Incomplete bracing, 41
+  Initial set, 88
+  Interference with traffic, 177
+
+  Jack arches, 29, 101
+  Joints in rails, 29, 109
+  -- in trough floors, 28, 180
+  Junction between metallic and masonry bridges, 183
+  -- -- new and old masonry bridges, 182
+  -- -- new and old metallic bridges, 180
+
+  Lattice girder stresses, 47-66
+  Liberal depth to girders, 23, 89, 184
+  Life of bridges, 165
+  Limit of elasticity, 61
+  Linen tapes, 172
+  Longitudinal floor girders, 23
+  Loose rivets, 21, 25, 51, 53, 56, 109
+
+  Main girders, 9-17
+  Masonry bridges, 157
+  -- enduring character of, 161
+  Memel timber, 150
+  Methods of calculation, 46, 61
+  -- of observing deflection, 90
+  -- of setting out deflection curves, 138
+  Movements of abutments, 158
+  -- of cast-iron bridge, 82
+  -- of piers, 42, 83, 159
+  -- of rollers, 7
+  -- of wrought-iron bridges, 4, 21, 38, 73
+
+  New members to old work, 116
+
+  Oiling steelwork, 99
+  Old drawings unreliable, 108
+  -- rivets, 21, 51, 54, 55
+  Open webs, 17
+  Overhead bracing, 39
+  -- girders, 118
+
+  Painting, 98
+  Parapets, 79
+  Permissible stress in old work, 110
+  Piers, movements of, 42, 83, 159
+  -- out of plumb, 159
+  Piles, decay of, 102, 150
+  Pitch pine, 28
+  Plasticity, 61
+  Plate webs, 9
+  Plated floors, 23, 25, 30
+  Pointing masonry, 164
+  Proposed rivet stresses, 58
+
+  Quickly applied loads, 89
+
+  Rail joints, 29, 109
+  Rails, breaks in, 30
+  Reaction of cross girder with centre support, 127
+  Red-lead, 98, 100
+  Relative merits of bridges, 169
+  Relief by centre girders, 122
+  Repainting, 100
+  Repair of bridges, 107, 147, 155, 163
+  -- of timber piles, 156
+  Replacing flange plates, 110
+  -- rivets, 111
+  Resistance of cast iron to rust, 101
+  Riveted connections, 45, 86
+  Rivets in cramped positions, 20
+  -- in cross girder ends, 21, 49, 53, 54
+  -- in road bridges, 60
+  -- in webs of main girders, 46
+  -- spacing of, 60, 80
+  -- stresses in, 56
+  Rocking of piers, 8, 83, 159
+  Roller bearings, 7
+  Rubble masonry, 161-164
+  Running load and deflection, 95
+  Rusting, instances of, 29, 96
+  -- of steelwork, 99
+  -- over sea-water, 98
+
+  Sag in timber bridges, 150
+  -- of tapes, 172
+  Scour under piers, 161
+  Sea piers, 42, 102
+  Setting bedstones, 3, 129, 176
+  Settlements, 76, 157
+  Skew bearings, 4
+  -- bridges, right and left, 173
+  -- -- floors, 25
+  Skirting plate, 26
+  Slope of girder ends, 92
+  Softening of cast-iron in sea-water, 101
+  Spacing of rivets, 60, 79
+  Spread of abutments, 157
+  Spring joints, 23
+  Steel trough girders, 68
+  -- troughing, 70
+  Stiffening girders from floor, 12, 40
+  -- to webs, 16, 38, 185
+  Stop piers, 158
+  Strength of light top booms, 40
+  Strengthening of bridges, 107, 122
+  -- bridge floors, 118
+  -- cross girders, 123
+  Stress in plated floors, 31
+  Study of old bridges, 185
+
+  Tall piers, 42, 159
+  Timber bridges, 149
+  -- floors, 27
+  -- staging, 177
+  Top booms, 18
+  Traffic during reconstruction, 177
+  Transverse bracing, 34, 117
+  Trough floors, 27, 180
+  -- girders, 50, 74
+  [T] stiffeners, breaks in, 16
+  Twin girders, 15, 75
+  Twisting of girders, 11, 68, 73
+  -- -- -- corrected, 12
+  Types of reconstruction, 174
+
+  [U]-shaped booms, 18
+  Uncomplicated stress, 62
+  Uniform pressure on bearings, 6
+
+  Value of E in deflection formul�, 87
+  Vibration, 162
+
+  Wasted webs, 14, 29, 96
+  Water, scour of, 161
+  Web buckling, 16
+  -- plates, cracked, 13, 14, 15, 50
+  -- rivets, 46, 50
+  -- stiffening, 16, 38, 185
+  Widening masonry bridges, 182
+  -- metallic bridges, 179
+  Wide spaced rivets, 79
+  Wind pressure, 41, 43
+
+  Yielding of piers, 8, 83, 159
+
+
+  LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
+  GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
+
+
+
+
+Transcriber's Notes:
+
+The text of the original work (including inconsistent spelling,
+hyphenation, formatting etc.) has been retained, except as mentioned
+below.
+
+The slight differences between the Table of Contents and the text have
+not been changed.
+
+Changes made to the text:
+
+Some punctuation errors and obvious typographical errors have been
+corrected silently.
+
+Several illustrations have been moved to where they are described in the
+text.
+
+Page 123, formula (2): the original shows an unclear superscript after
+the first L. As described in the following line of the text, this has
+been changed to L{_l_}.
+
+
+
+
+
+End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
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+<pre>
+
+Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Anatomy of Bridgework
+
+Author: William Henry Thorpe
+
+Release Date: December 6, 2013 [EBook #44371]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ANATOMY OF BRIDGEWORK ***
+
+
+
+
+Produced by Chris Curnow, Harry Lam� and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+</pre>
+
+
+<div class="tnbox">
+<p class="center">Please see the <a href="#TN">Transcriber&#8217;s Notes</a> at the end of this text.</p>
+</div>
+
+<hr class="chap" />
+
+<div class="noilloblock">
+<div class="figcenter">
+<img src="images/cover-b.jpg" alt="cover" width="366" height="550" />
+</div>
+<hr class="chap" />
+</div>
+
+<p><span class="pagenum"><a name="Page_v" id="Page_v"></a></span></p>
+<h1>THE<br />
+ANATOMY OF BRIDGEWORK</h1>
+
+<hr class="chap" />
+
+<p class="center highline blankabove"><span class="fsize125">THE</span><br />
+<span class="fsize175">ANATOMY OF BRIDGEWORK</span></p>
+
+<p class="center highline">BY</p>
+
+<p class="center blankabove"><span class="fsize150">WILLIAM HENRY THORPE</span><br />
+ASSOC. M. INST. C. E.</p>
+
+<p class="center highline blankabove blankbelow sstype">WITH 103 ILLUSTRATIONS</p>
+
+<div class="figcenter">
+<img src="images/illo003.png" alt="logo" width="150" height="176" />
+</div>
+
+<p class="center blankabove"><span class="oldtype">London</span><br />
+E. &amp; F. N. SPON, <span class="smcap">Limited</span>, 57 HAYMARKET<br />
+<span class="oldtype">New York</span><br />
+SPON &amp; CHAMBERLAIN, 123 LIBERTY STREET<br />
+1906</p>
+
+<hr class="chap" />
+
+<h2>PREFACE</h2>
+
+<p>In offering this little book to the reader interested in
+Bridgework, the author desires to express his acknowledgments
+to the proprietors of &#8220;Engineering,&#8221; in which journal
+the papers first appeared, for their courtesy in facilitating
+the production in book form.</p>
+
+<p>It may possibly happen that the scanning of these pages
+will induce others to observe and collect information extending
+our knowledge of this subject&mdash;information which,
+while familiar to maintenance engineers of experience, has
+not been so readily available as is desirable.</p>
+
+<p>No theory which fails to stand the test of practical
+working can maintain its claims to regard; the study of
+the behaviour of old work has, therefore, a high educational
+value, and tends to the occasional correction of views which
+might otherwise be complacently retained.</p>
+
+<p><span class="padl2">60 <span class="smcap">Winsham Street</span>,</span><br />
+<span class="padl4"><span class="smcap">Clapham Common, London, S.W.</span></span><br />
+<span class="padl6"><i>October</i>, 1906.</span></p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_vi" id="Page_vi"></a><br /><a name="Page_vii" id="Page_vii">[vii]</a></span></p>
+
+<h2>CONTENTS</h2>
+
+<table class="toc" summary="ToC">
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER I.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">INTRODUCTION&mdash;GIRDER BEARINGS.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="right fsize80">PAGE</td>
+</tr>
+
+<tr>
+<td class="subjects">Pressure distribution&mdash;Square and skew bearings&mdash;Fixed bearings&mdash;Knuckles&mdash;Rollers&mdash;Yield of supports</td>
+<td class="pagenr"><a href="#Page_1">1</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER II.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">MAIN GIRDERS.</td>
+</tr>
+
+<tr>
+<td class="subjects"><i>Plate webs</i>: Improper loading of flanges&mdash;Twisting of girders&mdash;Remedial measures&mdash;Cracks in webs&mdash;Stiffening of webs&mdash;<span class="lettsymb">T</span> stiffeners</td>
+<td class="pagenr"><a href="#Page_9">9</a></td>
+</tr>
+
+<tr>
+<td class="subjects"><i>Open webs</i>: Common faults&mdash;Top booms&mdash;Buckling of bottom booms&mdash;Counterbracing&mdash;Flat members</td>
+<td class="pagenr"><a href="#Page_17">17</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER III.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">BRIDGE FLOORS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Liability to defects&mdash;Impact&mdash;Ends of cross and longitudinal girders&mdash;Awkward riveting&mdash;Fixed ends to cross girders&mdash;Plated floor&mdash;Liberal depths desirable&mdash;Type connections&mdash;Effect of &#8220;skew&#8221; on floor&mdash;Water-tightness&mdash;Drainage&mdash;Timber floors&mdash;Jack arches&mdash;Corrugated sheeting&mdash;Ballast&mdash;Rail joints&mdash;Effect of main girders on floors</td>
+<td class="pagenr"><a href="#Page_20">20</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER IV.<span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">BRACING.</td>
+</tr>
+
+<tr>
+<td class="subjects">Effect of bracing on girders&mdash;Influence of skew on bracing&mdash;Flat bars&mdash;Overhead girders&mdash;Main girders stiffened from floor&mdash;Stiffening of light girders&mdash;Incomplete bracing&mdash;Tall piers&mdash;Sea piers</td>
+<td class="pagenr"><a href="#Page_34">34</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER V.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">RIVETED CONNECTIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Latitude in practice&mdash;Laboratory experiments&mdash;Care in considering practical instances&mdash;Main girder web rivets&mdash;Lattice girders investigated&mdash;Rivets in small girders&mdash;Faulty bridge floor&mdash;Stresses in rivets&mdash;Cross girder connections&mdash;Tension in rivets&mdash;Defective rivets&mdash;Loose rivets&mdash;Table of actual rivet stresses&mdash;Bearing pressure&mdash;Permissible stresses&mdash;Proposed table&mdash;Immunity of road bridges from loose rivets&mdash;Rivet spacing</td>
+<td class="pagenr"><a href="#Page_45">45</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VI.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">HIGH STRESS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Elastic limit&mdash;Care in calculation&mdash;Impact&mdash;Examples of high stress&mdash;Early examples of high stress in steel girders&mdash;Tabulated examples&mdash;General remarks</td>
+<td class="pagenr"><a href="#Page_61">61</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DEFORMATIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Various kinds&mdash;Flexing of girder flanges&mdash;Examples&mdash;Settlement deformations&mdash;Creeping&mdash;Temperature changes&mdash;Local distortions&mdash;Imperfect workmanship&mdash;Deformation of cast-iron arches</td>
+<td class="pagenr"><a href="#Page_73">73</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER VIII.<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DEFLECTIONS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Differences as between new work and old&mdash;Influence of booms and web structure on deflection&mdash;Yield of rivets and stiffness of connections&mdash;Working formul&aelig;&mdash;Set&mdash;Effect of floor system&mdash;Deflection diagrams&mdash;Loads quickly applied&mdash;&#8220;Drop&#8221; loads&mdash;Flexible girders&mdash;Measuring deflections&mdash;New method of observing deflections&mdash;Effect of running load</td>
+<td class="pagenr"><a href="#Page_85">85</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER IX.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">DECAY AND PAINTING.</td>
+</tr>
+
+<tr>
+<td class="subjects">Examples of rusting of wrought-iron girders&mdash;Girder over sea-water&mdash;Rate of rusting&mdash;Steelwork&mdash;Precautions&mdash;Red-lead&mdash;Repainting&mdash;Scraping&mdash;Girders built into masonry&mdash;Cast iron&mdash;Effect of sea-water on cast iron&mdash;Examples&mdash;Tabulated observations&mdash;Percentage of submersion&mdash;Quality of metal</td>
+<td class="pagenr"><a href="#Page_96">96</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER X.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Purpose&mdash;Methods of examination&mdash;Calculations&mdash;Stress in old work&mdash;Methods of reducing stress&mdash;Repair&mdash;Loose rivets&mdash;Replacing wasted flange plates&mdash;Adding new to old sections&mdash;Principles governing additions&mdash;Example&mdash;Strengthening lattice girder bracings&mdash;Bracing between girders&mdash;Strengthening floors&mdash;Distributing girders</td>
+<td class="pagenr"><a href="#Page_107">107</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XI.<span class="pagenum"><a name="Page_x" id="Page_x">[x]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Principal methods in use&mdash;Method of calculation&mdash;Adjustments&mdash;Connections&mdash;Method of execution&mdash;Checks&mdash;Effect of skew on method considered&mdash;Results of calculation for a typical case&mdash;Probable error&mdash;Practical examples&mdash;Special case&mdash;Method of determining flexure curves</td>
+<td class="pagenr"><a href="#Page_122">122</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">CAST-IRON BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Limitations of cast iron&mdash;Stress examples&mdash;Advantages and disadvantages&mdash;Foundry stresses&mdash;Examples&mdash;Want of ductility of cast iron&mdash;Repairs&mdash;Restricted possibilities</td>
+<td class="pagenr"><a href="#Page_141">141</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XIII.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">TIMBER BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Perishable nature&mdash;Causes of decay&mdash;Sag&mdash;Lateral bracing&mdash;Piles&mdash;Uncertainty respecting decay&mdash;Examples&mdash;Conditions and practice favourable to durability&mdash;Bracing&mdash;Protection&mdash;Repair&mdash;Piles&mdash;Cost</td>
+<td class="pagenr"><a href="#Page_149">149</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XIV.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">MASONRY BRIDGES.</td>
+</tr>
+
+<tr>
+<td class="subjects">Definition&mdash;Cause of defects or failure&mdash;Spreading of abutments&mdash;Closing in&mdash;Example&mdash;Stop piers&mdash;Example of failure&mdash;Strength of rubble arch&mdash;Equilibrium of arches&mdash;Effect of vibration on masonry&mdash;Safety centring&mdash;Methods of repair&mdash;Pointing&mdash;Rough dressed stonework</td>
+<td class="pagenr"><a href="#Page_157">157</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XV.<span class="pagenum"><a name="Page_xi" id="Page_xi">[xi]</a></span></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">LIFE OF BRIDGES&mdash;RELATIVE MERITS.</td>
+</tr>
+
+<tr>
+<td class="subjects">Previous history&mdash;Causes of limited life&mdash;Tabulated examples of short-lived metallic bridges&mdash;Timber and masonry bridges&mdash;Durability&mdash;Maintenance charges&mdash;First cost&mdash;Comparative merits&mdash;Choice of material</td>
+<td class="pagenr"><a href="#Page_165">165</a></td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapnr">CHAPTER XVI.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">RECONSTRUCTION AND WIDENING OF BRIDGES.</td>
+</tr>
+
+<tr>
+<td colspan="2" class="chapname">CONCLUSION.</td>
+</tr>
+
+<tr>
+<td class="subjects">Measuring up&mdash;Railway under-bridges&mdash;Methods of reconstruction in common use&mdash;Reconstruction of bridges of many openings&mdash;Timber staging&mdash;Traffic arrangements&mdash;Sunday work&mdash;Railway over-bridges&mdash;Widenings&mdash;Junction of new and old work&mdash;Concluding remarks&mdash;Study of old bridgework</td>
+<td class="pagenr"><a href="#Page_172">172</a></td>
+</tr>
+
+<tr>
+<td class="left blankabove">INDEX</td>
+<td class="pagenr"><a href="#Page_187">187</a></td>
+</tr>
+
+</table>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p>
+
+<p class="center highline blankabove blankbelow"><b><span class="fsize125">THE</span><br />
+<span class="fsize175">ANATOMY OF BRIDGEWORK.</span></b></p>
+
+<hr class="chap" />
+
+<h2>CHAPTER I.<br />
+<span class="chaptitle">INTRODUCTION.</span></h2>
+
+<p>No book has, so far as the author is aware, been written
+upon that aspect of bridgework to be treated in the following
+pages. No excuse need, therefore, be given for adding to
+the already large amount of published matter dealing with
+bridges. Indeed, as it too often happens that the designing
+of such constructions, and their after-maintenance, are in
+this country entirely separated, it cannot but be useful to
+give such results of the behaviour of bridges, whether new
+or old, as have come under observation.</p>
+
+<p>In the early days of metallic bridges there was of necessity
+no experience available to guide the engineer in his
+endeavour to avoid objectionable features in design, and he
+was, as a result, compelled to rely upon his own foresight
+and judgment in any attempt to anticipate the effects of
+those influences to which his work might later be subject.
+How heavily handicapped he must have been under these
+conditions is evident from the mass of information since
+acquired by the experimental study of the behaviour of
+metals under stress, and the growth of the literature of
+bridgework during the last forty years. That many mistakes
+were made is little occasion for surprise; rather is it a cause<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span>
+for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the
+study of defects and failures, even though they be of such a
+character that no experienced designer would now furnish
+like examples.</p>
+
+<p>Modern instances may, none the less, be found, with
+faults repeated, which should long since have disappeared
+from all bridgework, and are only to be accounted for by
+the unnatural divorce of design and maintenance already
+referred to. As the reader proceeds, it may appear that
+details are occasionally touched upon of a character altogether
+too crude and objectionable to need comment; but the
+consideration of these cases is none the less interesting, and,
+so far as the author&#8217;s observation goes, not altogether unnecessary.</p>
+
+<p>Most of the instances cited are of bridges, or parts of
+bridges, of quite small dimensions; but it is these which
+most commonly give trouble, both because the effects of impact
+are in such cases most severely felt, and possibly because
+the smaller class of bridges is very generally designed by men
+of less experience, than large and imposing structures.</p>
+
+<p>The particulars given relate in all cases to bridges of
+wrought iron, unless otherwise described.</p>
+
+<p>An endeavour has been made to secure some kind of
+order in dealing with the subject, but it has been found
+difficult to avoid a somewhat disjointed treatment, inseparable,
+perhaps, from the nature of the matter. Finally,
+the reader may be assured that every case quoted has come
+under the writer&#8217;s personal notice.</p>
+
+<h3><span class="smcap">Girder Bearings.</span></h3>
+
+<p>In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing
+allowed. Clearly, the surface over which the pressure<span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span>
+is distributed should be sufficiently ample to avoid overloading
+and possible crushing or fracture of bedstones where
+these exist; but if no knuckles are introduced, this is an
+extremely difficult matter to insure. A long bearing may
+deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.</p>
+
+<p>If the girder is made with truly level bearings, and the
+beds set level, it will certainly, when under load, throw an
+extreme pressure upon that part of the bearing surface
+immediately under the forward edge of the bearing-plate.
+These considerations probably account for bedstones frequently
+cracking, in addition to which possibility there is
+the disadvantage that the designer does not know where the
+girder will rest, and cannot truly define the span. The
+variation of flange-stress due to this cause may, in a girder
+of ordinary proportions, having bearings equal in length to
+the girder&#8217;s depth, be as much as 15 per cent. above or
+below that intended.</p>
+
+<p>If great care be taken in setting beds, in the first instance,
+to dip toward the centre of the span an amount depending
+upon the anticipated girder deflection, it may be possible to
+insure that when under full load the girder bearing shall
+rest equally upon its seat; but this is evidently a difficult
+condition to obtain practically, is good only for one degree of
+loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence
+of a slight leaning forward of abutment walls.</p>
+
+<p>Double or treble thicknesses of hair-felt are sometimes
+placed beneath girder bearings, with the object of securing
+a better distribution of pressure, no doubt with advantage;
+but this practice, though it may be quite satisfactory as
+applied to girders carrying an unchangeable load, hardly
+meets the case for loads which are variable. Notwithstanding
+the faulty nature of the plain bearing ordinarily used<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span>
+for girders of moderate span, its extreme simplicity commends
+it to most engineers. It must be admitted that no serious
+inconvenience need be anticipated in the majority of cases,
+particularly if the bearings are limited in length, do not
+approach nearer than 3 inches to the face of bedstones, and
+are furnished with hair-felt or similar packing.</p>
+
+<div class="figcenter"><a name="Fig1" id="Fig1"></a>
+<img src="images/illo016.png" alt="" width="450" height="216" />
+<p class="caption"><span class="smcap">Fig.</span> 1.</p>
+</div>
+
+<p>Whether with long or short bearings, the forward edge
+should be at right angles to the girder&#8217;s length. In skew
+bridges it is sometimes seen that this edge follows the angle
+of skew. The effect on the girder is to twist it, as will be
+clear from a little consideration. In evidence of this the
+case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment
+right up to the masonry face at a rather bad angle (about
+15 degrees), was, after twenty years, found canted over at
+the top to the extent of 4 inches, with the further result of
+springing a joint in the top flange at about the middle of
+the girder, causing some rivets to loosen. The bedstone
+was also very badly broken at the face, and had to be
+replaced in the course of repairs (<a href="#Fig1">Fig. 1</a>). This girder had,
+in addition to the canting from the upright position at its
+end, and the distortion of the top flange, a curvature in the
+same direction, though less in amount, at the bottom&mdash;an<span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span>
+effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder
+end to creep along the abutment away from the point at
+which it bears hardest, under frequent applications and
+removals of the live load, and accompanying deflections.</p>
+
+<p>This tendency to travel may be aggravated in bridges
+carrying a ballasted road, in which there may be a considerable
+thickness of ballast near the bearings, by the compacting
+and spreading of this material taking effect upon the
+girder end, tending to push it outwards, being tied only by
+a few light cross-girders badly placed for useful effect.
+The movement may be prevented in new work for moderate
+angles of skew by carrying the end cross-girders well back,
+and securing them in some efficient manner; or by the
+introduction of a diagonal tie following the skew face, and
+attached to cross and main girder flanges (<a href="#Fig2">Fig. 2</a>)&mdash;a method
+which may be applied to existing work also.</p>
+
+<div class="figcenter"><a name="Fig2" id="Fig2"></a>
+<img src="images/illo017.png" alt="" width="350" height="232" />
+<p class="caption"><span class="smcap">Fig.</span> 2.</p>
+</div>
+
+<p>For such a case as that cited it is imperative that ballast
+pressure at the girder end should be altogether eliminated.</p>
+
+<p>The fixing of girder ends by bolts&mdash;a practice at one
+time usual&mdash;hardly calls for remark, as it is now seldom
+resorted to unless for special reasons; but it may be well to
+point out the weakening effect of holes for any purpose in<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span>
+bedstones. Bed-plates commonly need no fixing; the weight
+carried keeps them in position, or if, in the case of very
+light girders upon separate plates, it is considered well to
+secure these from shifting, it may best be done by letting
+the plate in bodily a small amount, or by means of a very
+shallow feather sunk into a chase.</p>
+
+<div class="figcenter"><a name="Fig3" id="Fig3"></a>
+<img src="images/illo018.png" alt="" width="450" height="298" />
+<p class="caption"><span class="smcap">Fig.</span> 3.</p>
+</div>
+
+<p>As an improvement upon the plain bearing usually
+adopted, it is an easy matter so to design girder-ends as to
+deliver the load by a narrow strip of bearing-plate carried
+across the bottom flange, distributing the pressure upon the
+stone, if there be one, by means of a simple rectangular plate
+of sufficient stoutness (<a href="#Fig3">Fig. 3</a>). An imperfect knuckle will
+by this means result, with freedom to slide, and the girder
+span be defined within narrow limits. A true knuckle is, of
+course, the best means of securing imposition of the load
+always in the same place; but this by itself is not sufficient
+where the girder is of a length to make temperature and
+stress variations important, in which case rollers, or freedom
+to slide, become necessary. Bridges exist in which roller-bearings
+have been adopted without the knuckle, or its<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span>
+equivalent, but this is wholly indefensible, as it is obvious
+that the forward roller will in all probability take the whole
+load, and cannot be expected to keep its shape and roll freely
+under this mal-treatment. It is sometimes asserted that
+rollers are never effective after some years&#8217; use; that they
+become clogged with dirt, and refuse to perform their office.</p>
+
+<p>There is no reason why rollers should not be boxed in to
+exclude dirt by a casing easily removed, some attention being
+given to them, and any possible accumulation of dirt removed
+each time the bridge is painted.</p>
+
+<p>To test the behaviour of rollers under somewhat unfavourable
+conditions for their proper action&mdash;that of the
+bearings of main roof trusses of crescent form, 190 feet span&mdash;the
+author, some thirty years since, took occasion to make
+the necessary observations, and found evidence of a moderate
+roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders
+resting upon columns, particularly if of cast iron, a roller
+and knuckle arrangement is most desirable for any but very
+small spans, as, if not adopted, the result will be a canting
+of the columns from side to side&mdash;a very small amount, it is
+true, but sufficient to throw the load upon the extreme edges
+of the base, though the knuckle alone will relieve the top of
+this danger. The author at one time took the trouble to
+examine, so far as it could be done superficially and without
+opening out the ground to make a complete inspection
+possible, a number of bridges crossing streets, in which
+girders rested upon and were secured to cast-iron columns
+standing in the line of kerb; and he found cracks, either at
+the top or bottom, in about one of every four columns.</p>
+
+<p>When girders passing over columns are not continuous,
+it may be difficult to find room for a double roller and
+knuckle arrangement; but this inconvenience may be overcome
+by carrying one girder-end wholly across the column-top,<span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span>
+and securing the next girder-end to it in a manner
+which a little care and ingenuity will render satisfactory,
+one free bearing then serving to carry the load from both
+girders.</p>
+
+<p>Though the wisdom of using rollers is apparent in spans
+exceeding some moderate length, say 80 feet&mdash;as to which
+engineers do not seem quite decided&mdash;and varying with the
+conditions, it need not be overlooked that in some cases
+masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will
+yield a small amount without injury, and though shorter, if
+resting upon a bottom not absolutely rigid, will rock and
+give the necessary relief; but it is obvious, if the resistance
+to movement is sufficiently great, and the girder cannot slide
+or roll on its bearings, bedstones will probably loosen, as,
+indeed, frequently happens.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span></p>
+
+<h2>CHAPTER II.<br />
+<span class="chaptitle">MAIN GIRDERS; PLATE-WEBS.</span></h2>
+
+<p>It is seldom that girders of this description&mdash;or, indeed, of
+any other&mdash;show signs of failure from mere defect of strength
+in the principal parts, even though somewhat highly stressed;
+and instances tending to support this statement will be given
+in a later chapter. For the present, it is proposed to indicate
+peculiarities of behaviour only, generally, but not always,
+harmless.</p>
+
+<p>Though now less often done, it was at one time common
+practice to load plate-girders on the bottom flange by simply
+resting floor timbers, rails, troughs, or cross-girders upon
+them. In outside girders one result of this is to cause the
+top flange to take a curve in plan, convex towards the road,
+every time the live load comes upon the floor of the bridge,
+upon the passing of which the flange resumes its figure, though
+still affected by that part of the load which is constant.</p>
+
+<p>A bridge of 47 feet span, carrying two lines of way,
+having one centre and two outside girders, with a floor consisting
+of old Barlow rails, resting upon the bottom flanges,
+showed the peculiarity named in a marked degree.</p>
+
+<p>The outside girders, under dead load only, were, as to
+the top flanges (see <a href="#Fig4">Figs. 4</a> and <a href="#Fig5">5</a>), 1<sup>1</sup>&#8260;<sub>4</sub> inch and 1<sup>1</sup>&#8260;<sub>16</sub> inch
+respectively out of straight in their length, but upon the
+passing of a goods engine and train curved an additional 1<sup>1</sup>&#8260;<sub>8</sub>
+inch, or 2<sup>3</sup>&#8260;<sub>8</sub> inches in all, for one outside girder, and 2<sup>3</sup>&#8260;<sub>16</sub>
+inches for the other.</p>
+
+<p>The centre girder, having a broader and heavier top<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span>
+flange, curved <sup>5</sup>&#8260;<sub>8</sub> inch towards whichever road might be
+loaded. The effect of such horizontal
+flexure is clearly to induce stresses of
+tension and compression in the flanges,
+which, being (for the top flange) compounded
+with the normal compressive
+stress due to load carried, results in a
+considerable want of uniformity across
+the section.</p>
+
+<div class="figcenter"><a name="Fig4" id="Fig4"></a>
+<img src="images/illo022.png" alt="" width="600" height="149" />
+<p class="caption"><span class="smcap">Fig.</span> 4.</p>
+</div>
+
+<p>In the case under notice, the writer
+estimates the stresses for an outer
+girder top flange at 4&middot;5 tons per
+square inch compression for simple
+loading, and 5&middot;5 tons per square inch
+of tension and compression, on the
+inner and outer edges, due to flexure,
+resulting when compounded in a stress
+of 1 ton per square inch tension on
+the inside, and 10 tons per square inch
+compression on the outside edge. In
+this rather extreme case the stress on
+the inner edge, or that nearest the
+load, is reversed in character.</p>
+
+<p>The effect described appears to be
+not wholly due to the twisting moment.
+It is apparent that whatever curvature
+may be induced by twisting alone
+must be aggravated in the compression
+flange by its being put out of line.</p>
+
+<p>The writer does not attempt here to
+apportion the two effects in any other
+way than to say that the greater part
+of the flexure appears to be due to the secondary cause. Consistent
+with this view of the matter is the fact that the inclination<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span>
+of the girder towards the rails greatly exceeded the
+calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the
+floor rails bore hard at their extreme ends, at which point of
+bearing the calculated twisting moment accounts for less
+than one-half of the flexure observed in the flanges.</p>
+
+<div class="figcenter"><a name="Fig5" id="Fig5"></a>
+<img src="images/illo023.png" alt="" width="400" height="321" />
+<p class="caption"><span class="smcap">Fig.</span> 5.</p>
+</div>
+
+<p>The girders upon removal in the course of reconstruction
+again took the straight form, showing that the very
+frequent development of the stresses named had not sensibly
+injured the metal, though the bridge carried as many as
+three hundred trains daily in each direction, and had done so
+for very many years.</p>
+
+<p>The deformation of the top flange only has been noticed,
+yet the same tendency exists in the bottom, though the actual
+amount is much less, both because the lower flanges are in
+tension, and are also in great degree confined by the frictional
+contact of the cross bearers, even where no proper ties
+are used. In the case dealt with the bottom flanges of
+the outer girders curved <sup>1</sup>&#8260;<sub>8</sub> inch outwards only.</p>
+
+<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p>
+
+<p>With the broad flanges commonly adopted in English
+practice, twisting of the girders, under conditions similar to
+the above, will not generally be a serious matter; but with
+narrow flanges possessing little lateral stiffness it might be a
+source of danger.</p>
+
+<div class="figc450"><a name="Fig6" id="Fig6"></a><a name="Fig7" id="Fig7"></a>
+<img src="images/illo024.png" alt="" width="450" height="282" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 6.</span>
+<span class="right49"><span class="smcap">Fig.</span> 7.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 6. and <span class="smcap">Fig.</span> 7.</p>
+</div>
+
+<p>The twisting may be limited in amount by introducing
+a cross-frame between the girders, from which they are
+stiffened; by strutting the girders immediately from the floor
+itself, in which case they cannot cant to a greater extent
+than that which corresponds to the floor deflection; or by
+designing the top flange to be unsymmetrical with reference
+to the web, as in <a href="#Fig6">Figs. 6 and 7</a>, with the object of insuring
+that under the joint effect of vertical loading and twisting,
+the stress in the flange shall at maximum loads be uniform
+across the section, and allow it to remain straight. This
+may be secured by making the eccentricity of the flange
+section equal to that of the loading. For instance, if the load
+be applied 3 inches away from the web centre, the flange
+should have its centre of gravity 3 inches on the other side
+of the centre line. It can be shown that this is true
+throughout the length of the girder, and irrespective of the
+depth. An instance in which flange eccentricity being in
+excess, curvature outwards resulted, will be found in a later<span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span>
+chapter on deformations, etc. It will not generally be
+necessary to make the bottom flange eccentric, as it is
+commonly tied in some way; but if done, the eccentricity
+should be on the same side as for the top. The flanges
+remaining straight under these conditions are not subject to
+the complications of stress referred to in the case first quoted.
+The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the
+kind discussed.</p>
+
+<p>It should be remarked that by the two first methods, if
+the stiffening frames are wide apart and attached direct to
+the web, there is a liability for this to tear, under distress,
+rather than keep the girder in line.</p>
+
+<p>There is one other possible consequence of throwing load
+upon the flanges of a girder of a much more alarming nature.
+In girders not very well stiffened, it may happen that the
+frequent application of load in this manner finally so injures
+the web-plate, just above the top edge of the bottom angle-bars,
+as to cause it to rip in a horizontal direction. More
+likely is this to happen with a centre girder taking load first
+on one side, then on the other, and again on both together.
+Cases may be cited in which cracks right through the webs
+3 feet or more in length have resulted from this cause. It
+is very probable, however, that in some of these cases the
+matter was aggravated by the use of a poor iron in the webs,
+as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a
+girder, would, if they could not be made thin enough, even
+encourage the use of an indifferent metal as being quite good
+enough for that part of the work.</p>
+
+<p>An instance of web-fracture from somewhat similar causes
+may be here given.</p>
+
+<p>In a bridge of 31 feet 6 inches effective span, and consisting
+of twin girders carrying rails between, as shown in <a href="#Fig8">Figs.
+8</a> and <a href="#Fig9">9</a>, the load resting upon the inner ledges, formed by<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span>
+the bottom flange, induced such a bending and tearing action
+along the web just above the angle-bars,
+as to cause a rip in one of the girders, well
+open for some distance, and which could
+be traced for 14 feet as a continuous crack.</p>
+
+<div class="figcenter"><a name="Fig8" id="Fig8"></a>
+<img src="images/illo026.png" alt="" width="600" height="101" />
+<p class="caption"><span class="smcap">Fig.</span> 8.</p>
+</div>
+
+<div class="figcenter"><a name="Fig9" id="Fig9"></a>
+<img src="images/illo027.png" alt="" width="450" height="309" />
+<p class="caption"><span class="smcap">Fig.</span> 9.</p>
+</div>
+
+<p>It will be noticed in the figure that the
+<span class="lettsymb">T</span> stiffeners occur only at the outer face of
+the web, and that the inner vertical strips
+stop short at the top edge of the angles,
+the result being that under load the flange
+would tend to twist around some point, say
+A, at each stiffener, inducing a serious stress
+in the thin web at that place, while away
+from these stiffeners the web would be
+more free to yield without tearing. The
+fact that at a number of the stiffeners
+incipient cracks were observed, some only
+a few inches long, suggests this view of
+the matter.</p>
+
+<p>A case of web-failure from other influences
+coming under notice showed breaks
+at the upper part of the web extending
+downwards.</p>
+
+<p>In this bridge, of 32 feet span, which
+had been in existence thirty-two years,
+the webs&mdash;originally <sup>1</sup>&#8260;<sub>4</sub> inch thick&mdash;were,
+largely because of cinder ballast in contact
+with them, so badly wasted as to be generally
+little thicker than a crown-piece, and
+in places were eaten through; in addition
+to which, the road being on a sharp curve,
+the rail-balks had been strutted from the
+webs to keep them in position, the effect
+of which would be to exert a hammering thrust upon the<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span>
+face of the web at the abutting ends, and assist in starting
+cracks in webs already much corroded. A feature of this case,
+tending to show that the breaks resulted as the joint effect of
+waste and ill-usage by the strut members, rather than by excessive
+stress in the web as reduced, is to be found in the fact that
+the girders when removed were observed to be in remarkably
+good shape&mdash;i.e. the camber, marked on the original drawings
+to be 1<sup>1</sup>&#8260;<sub>2</sub> inch, still showed as a perfectly even curve of that
+rise, which would hardly have been the case if the lower
+flange had been let down by web-rupture, the result of
+excessive web-stresses.</p>
+
+<p>Occasionally webs will crack through the solid unwasted
+plate, in a line nearly vertical; not where shear stress is
+greatest, but generally at some other place, and from no
+apparent cause, either of stress or ill-usage. The writer has
+observed this only in the case of small girders not exceeding
+2 feet in depth; and, for want of any better reason, attributes
+these cracks to poor material, coupled with some latent defect.
+In a bridge having some thirty cross-girders, each 26 feet
+long, about every other one had a web cracked in this
+manner after many years&#8217; use.</p>
+
+<p><span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span></p>
+
+<p>Web-cracks of the kind first indicated, are perhaps, the
+most probable source of danger in plate-girders, of any which
+are likely to occur. The fault is insidious, difficult to detect
+when first developed, and perhaps not seen at all till the
+bridge, condemned for some other reason, has the girders
+freely exposed and brought into broad light. The manner
+in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of
+these defects an uncertain matter, unless sufficient trouble is
+occasionally taken to render inspection complete.</p>
+
+<p>The manner in which girders with wasted and fractured
+webs will still hang together under heavy loading seems to
+warrant the deduction that, in designing new work, it can
+hardly be necessary to provide such a considerable amount of
+web-stiffening as is sometimes seen; experience showing that
+defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form
+of cracks.</p>
+
+<p>A case of web-buckling lies, so far, without the author&#8217;s
+experience. There is no need to introduce, for web-stresses
+alone, more stiffening than that which corresponds to making
+the stiffeners do duty as vertical struts in an openwork
+girder; in which case it is sufficient to insure that the
+stiffeners occurring in a length equal to the girder&#8217;s depth
+shall, as struts, be strong enough in the aggregate to take
+the whole shear force at the section considered, in no case
+exceeding this amount on one stiffener. For thin webs in
+which the free breadth is greater than one hundred and
+twenty times the thickness, the diagonal compressive stress
+may be completely ignored, and the thickness determined
+with reference to the diagonal tension stress only.</p>
+
+<p>There is one fault which frequently shows itself in
+stiffeners though not the result of web-stresses, and when
+performing an additional function&mdash;viz., the breaking of<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span>
+<span class="lettsymb">T</span> stiffener knees at the weld, where brought down on to the
+tops of cross-girders, due to the deflection of the floor, as
+shown in <a href="#Fig10">Fig. 10</a>. When such knees are used, the angle
+may properly be filled in with a gusset-plate to relieve the
+weld of strain and prevent fracture.</p>
+
+<div class="figcenter"><a name="Fig10" id="Fig10"></a>
+<img src="images/illo029.png" alt="" width="350" height="343" />
+<p class="caption"><span class="smcap">Fig.</span> 10.</p>
+</div>
+
+<p>There is some little temptation in practice to make use
+of the solid web as a convenient stop for ballast, or road
+material. Special means, perhaps at the cost of some little
+trouble, should be adopted, where necessary, to avoid this.</p>
+
+<h3><span class="smcap">Main Girders; Open Webs.</span></h3>
+
+<p>With these, as with plate-girders, deficiency of strength&mdash;i.e.
+of section strength&mdash;is seldom so marked as to be a
+reasonable cause of anxiety. In particular instances faults
+in design may result in stresses of an abnormal amount,
+though rarely to an extent occasioning any ill effects. The
+practice of loading the bottom flanges at a distance from<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span>
+the centre, the bad effects of which have already been dealt
+with as applied to plate-girders, is not commonly resorted to
+in girders having open webs, nor are these so liable to be
+heaped with ballast in immediate proximity to essential
+members of the structure.</p>
+
+<p>Some defects are, however, occasionally seen which may
+be remarked. Top booms of an inverted <span class="lettsymb">U</span> section are
+sometimes made with side webs too thin, and having the
+lower edges stiffened insufficiently, or not at all. Where
+this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to
+sustain the compressive stress to which the rest of the boom
+is liable. The practice of putting the greater part of the
+boom section in an outer flange, characteristic of this defect,
+has the further disadvantage of throwing the centre of gravity
+of the section so near its outer edge as to make impracticable
+the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section
+is thrown into the flange-plates, the centre of gravity of the
+section has no constant position along the boom&mdash;an additional
+inconvenience where correct design is aimed at.</p>
+
+<p>These considerations indicate the propriety of arranging
+the bulk, or all, of the section at the sides, thus reducing or
+getting rid of the objections named.</p>
+
+<p>Where the bottom boom consists of side plates, only one
+point demands attention. It is found that, though nominally
+in tension, the end bays are liable occasionally to buckle, as
+though under compressive stress, and need stiffening, not
+excepting girders which at one end are mounted on rollers.
+This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes,
+such as wind forces, or as in the case of a bridge carrying a
+railway, in which the rigidity of the permanent-way may be
+such that the bridge-structure, in extending towards the<span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span>
+roller end, cannot move it sufficiently, causing a reversal of
+stress on the lighter portions of the bottom boom at the
+knuckle end; or by the exposed girder booms becoming
+very sensibly hotter than the bridge floor, and by expanding
+at a greater rate, cause this effect, from which rollers cannot
+protect them.</p>
+
+<p>In counterbracing consisting of flat bars it is desirable
+either to secure these where they cross other members, or
+stiffen them in some manner to avoid the disagreeable
+chattering which will otherwise commonly be found to occur
+on the passage of the live load.</p>
+
+<p>Occasionally diagonal ties are made up of two flat bars
+placed face to face, to escape the use of one very thick
+member. Where this is done, the two thicknesses, if not
+riveted together along the edges, will be liable to open, as
+the result of rusting between the bars in contact, when the
+evil will be aggravated by the greater freedom with which
+moisture will enter the space.</p>
+
+<p>Other matters relating to open-web girders will be more
+conveniently dealt with under their separate headings, particularly
+a further consideration of the relationship subsisting
+between the booms and floor structure.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span></p>
+
+<h2>CHAPTER III.<br />
+<span class="chaptitle">BRIDGE FLOORS.</span></h2>
+
+<p>The floors of bridges commonly give more trouble in maintenance,
+and their defects are more frequently the cause
+which renders reconstruction necessary, apart from reasons
+not concerning strength, than any other part of such structures.
+When it is considered that this portion of a bridge
+is first affected by impact of the load which comes upon it,
+and is usually light in comparison with the main girders
+further removed from the load, and to which the latter is
+transferred through the more or less elastic floor, the fact
+will be readily appreciated by those not already familiar
+with it.</p>
+
+<p>The end attachments of cross and longitudinal girders
+are very liable to suffer by loosening of rivets, or, more
+rarely, by breaking of the angle-irons which commonly make
+such a connection. A not unusual defect of old work, which
+may also sometimes be seen in work quite new, where the
+cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends.
+There is small chance of these ever being properly tight, if
+the act of riveting is rendered difficult by bad design. This
+is the more objectionable if it happens that cross-girder ends
+abut against opposite sides of the web of an intermediate
+main girder, and are secured by the same rivets passing
+through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which
+they become subject, as the cross-girders take their load and<span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span>
+deflect under it, will be very apt to loosen them. The author
+has seen a case of this kind (see <a href="#Fig11">Figs. 11</a> and <a href="#Fig12">12</a>)&mdash;rather
+extreme, it is true&mdash;in which nearly the whole of the cross-girder
+end rivets were loose, some nearly worn through, thus
+allowing the cross-girders to be carried, not by their attachments,
+but by resting upon the main-girder flanges, which
+in turn, by repeated twisting, tore the web for a length of
+4 feet; there was also pronounced side flexure of the top
+booms. The movements generally on this bridge (of 42-feet
+span), whether of main or cross-girders, were very considerable
+and disturbing. It was removed after about twenty-three
+years&#8217; use.</p>
+
+<div class="figcenter"><a name="Fig11" id="Fig11"></a>
+<img src="images/illo033a.png" alt="" width="400" height="259" />
+<p class="caption"><span class="smcap">Fig.</span> 11.</p>
+</div>
+
+<div class="figcenter"><a name="Fig12" id="Fig12"></a>
+<img src="images/illo033b.png" alt="" width="400" height="96" />
+<p class="caption"><span class="smcap">Fig.</span> 12.</p>
+</div>
+
+<p>There is no necessity, as a rule, for the ends of cross-girders
+attached to the same main girder at opposite sides
+to be placed in line. The author prefers to arrange them to
+miss, by which device each connection is entirely separate,<span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span>
+the riveting can be more efficiently executed, erection is
+simplified, and the rivets will be more likely to keep tight.
+Other special cases of cross-girder ends will be dealt with
+under the head &#8220;<a href="#Page_45">Riveted Connections</a>.&#8221;</p>
+
+<p>It is sometimes contended that cross-girders attached at
+their ends by a riveted connection should be designed as for
+fixed ends, in which case they are usually made of the same
+flange section throughout, with a view to satisfy the supposed
+requirements. But a girder to be rightly considered
+as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction,
+and no overhead bracing, this is so far from being
+the case as to leave little occasion for taking the precaution
+named. As the cross-girders deflect, the main girders will
+commonly yield slightly, inclining bodily towards the cross-girders,
+if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in
+this manner is usually less than that which corresponds to
+fixing the cross-girder ends, and is, generally, slight. It is,
+of course, necessary that this measure of resistance at the
+connection should be borne in mind for the sake of the joint
+itself, quite apart from any question of fixing.</p>
+
+<p>Possibly, in quite exceptional cases, where very stiff
+main girders are braced in such a manner as to prevent
+canting, it may be proper to consider the cross-girder ends
+as fixed, or for those near the bearings of heavy main
+girders; but the author has not met with any example
+where cross-girders, apart from attachments, appear to have
+suffered from neglect of this consideration.</p>
+
+<p>With cross-girders placed on either side of a main girder,
+and in line, it may also, for new work, be desirable to regard
+the ends as fixed, and to detail them with this in view. It
+does not, however, appear wise to carry this assumption to
+its logical issue, and reduce the flange section to any appreciable<span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span>
+extent on this account. The fixity of the ends will, in
+any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a
+moderate effect in reducing flange stress at the middle of
+the loaded floor beam.</p>
+
+<div class="figc450"><a name="Fig13" id="Fig13"></a><a name="Fig14" id="Fig14"></a><a name="Fig15" id="Fig15"></a>
+<img src="images/illo036.png" alt="" width="450" height="315" />
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 13.</span>
+<span class="center34"><span class="smcap">Fig.</span> 14.</span> <span class="right25"><span class="smcap">Fig.</span> 15.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 13., <span class="smcap">Fig.</span> 14. and <span class="smcap">Fig.</span> 15.</p>
+</div>
+
+<p>Similar reasons affect the design of longitudinal girder
+attachments to cross-girders, which, if intended to support
+rails, cannot of necessity be schemed to come other than in
+line. Where the floor is plated as one plane surface, there
+will not usually be any trouble resulting if no special precautions
+are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving
+the joints of abnormal stress. If the plating is, however,
+designed in a manner which does not present this advantage,
+or if the floor be of timber, it is better to decide whether
+the connections shall be considered as fixed, and made so;
+or avowedly flexible, and detailed in such a manner as to
+possess a capacity for yielding slightly without injury.
+Those connections are most likely to suffer which are neither
+of the one character nor the other, offering resistance without
+the ability to maintain it. <a href="#Fig13">Figs. 13</a>, <a href="#Fig14">14</a>, and <a href="#Fig15">15</a> give representations
+of three &#8220;spring joint&#8221; methods of insuring yield
+in a greater or less degree. For small longitudinals it is,
+perhaps, sufficient to use end angles with very broad flanges
+against the cross-girder web; these to be riveted in the
+manner indicated in <a href="#Fig15">Fig. 15</a>.</p>
+
+<p>Liberal depth to floor beams is distinctly advantageous
+where it can be secured, rendering it easier to design the ends
+in a suitable manner, by giving room near mid-depth of the
+attachment to get in the necessary number of rivets; or
+where the ends are rigidly attached direct to vertical
+members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with
+a correspondingly reduced cant of the main girders and<span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span>
+flexure of the vertical member, with smaller consequent
+secondary stresses. In any case deep girders will contribute
+to stiffness of the floor itself, favourable in railway bridges
+to the maintenance of permanent-way in good order.</p>
+
+<div class="figcenter"><a name="Fig16" id="Fig16"></a><a name="Fig17" id="Fig17"></a><a name="Fig18" id="Fig18"></a>
+<img src="images/illo037.png" alt="" width="450" height="312" />
+<p class="caption"><span class="smcap">Figs.</span> 16, 17, 18.</p>
+</div>
+
+<p>A point in connection with skew-bridge floors occasionally
+overlooked is the combined effect of the skew, and main
+girder camber, in throwing the floor structure out of truth,
+if no regard has been paid to this. The result is bad cross-girder
+or other connections; or, in the case of bearers running
+over the tops of main girders, a necessity for special
+packings to bring all fair (<a href="#Fig17">Fig. 17</a>). The author has in such
+cases, where cross-girders are used, set the main girder beds
+at suitable levels, in order that the cross-bearers may all be
+horizontal (see <a href="#Fig16">Figs. 16</a> and <a href="#Fig18">18</a>). This may not always be
+permissible; but, however the difficulty may be met, it
+should be dealt with as part of the design. For small angles
+of skew only may it be neglected.</p>
+
+<p>Rivets attaching cross-girder angles to the web will occasionally<span class="pagenum"><a name="Page_25" id="Page_25">[25]</a></span>
+loosen, probably due in most cases to bad work,
+together with some circumstance of aggravation, as in the
+case of a bridge floor consisting of girders spaced 3 feet 6
+inches apart, with short timber bearers between, carrying
+rails. In many girders the top row of rivets, of ordinary
+pitch and size, had loosened, allowing the web, about <sup>1</sup>&#8260;<sub>4</sub> inch
+thick, a movement of <sup>1</sup>&#8260;<sub>8</sub> inch vertically. The rails being
+very close down upon the cross-girder tops, though not intended
+to touch, had at some time probably done so, and by
+&#8220;hammering&#8221; produced the result described.</p>
+
+<p>Plated floors are often found which are objectionable on
+account of their inability to hold water, arising sometimes
+from bad work, as often from wide spacing of rivets. With
+rivets arranged to be easily got at, and pitched not more
+than 3 inches apart, a tight floor may be expected; but it is
+still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside
+of the plate, and sufficiently long to deliver direct into
+gutters, where these are necessary. Drain-holes should not
+be less frequent than one to every 50 square feet of floor, if
+flat, and may advantageously be more so. Gutters should<span class="pagenum"><a name="Page_26" id="Page_26">[26]</a></span>
+slope well, and care be taken to insure practicable joints and
+good methods of attachment&mdash;a matter too often left to
+take care of itself, with considerable after-annoyance as a
+result.</p>
+
+<p>The use of asphalt, or asphalt concrete, to render a
+plated floor water-tight is hardly to be relied upon for railway
+bridges, though no doubt effective for those carrying
+roads. It is extremely difficult to insure that it shall stand
+the jarring and disturbance to which it may be subject, and
+under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying
+of the floor. In bulk, as in troughs, it may be useful, but
+in thin coverings on plates it cannot be depended upon.</p>
+
+<p>Floors having plated tops are sometimes finished over
+abutments or piers in a manner which is not satisfactory,
+either as regards the carrying of loads or accessibility for
+painting. If the plates are carried on to a dwarf wall with
+the intention that the free margin of the plate shall rest
+upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after
+the girder work is in place, making it difficult to insure that
+the wall really supports the plate, the result being that this
+may have to carry itself as best it can. In any case, severe
+corrosion will occur on the underside, and the plate rust
+through much before the rest of the floor; the masonry also
+will usually be disturbed.</p>
+
+<p>It appears preferable to form the end of the floor with a
+vertical skirting-plate having an angle or angles along the
+lower edge. This may come down to a dwarf wall, but preferably
+not to touch it, the skirting being designed to act
+as a carrying girder. A convenient arrangement is shown in
+<a href="#Fig19">Fig. 19</a>, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the
+skirting referred to being carried continuously along the<span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span>
+floor edge, and attached to each girder-web, the whole of the
+more important parts being open to the painter.</p>
+
+<div class="figcenter"><a name="Fig19" id="Fig19"></a>
+<img src="images/illo039.png" alt="" width="400" height="326" />
+<p class="caption"><span class="smcap">Fig.</span> 19.</p>
+</div>
+
+<p>Trough floors consisting of one or other of the forms of
+pressed or rolled section present the objection that it is almost
+impracticable to arrange an efficient connection at the ends,
+if they abut against main girders, and but little connection
+is, as a rule, attempted, and sometimes none. The result is
+that the load from these troughs is delivered in an objectionable
+manner, and the ends being open or imperfectly closed,
+water and dirt escape on to the flange, or other ledge, which
+supports them. A description of pressed floor which promises
+to overcome this objection, and provide a ready means
+of attachment to the webs of plate-girders, or of booms
+having vertical plate-webs, has within the last few years been
+introduced. This has the ends shaped in such a manner as
+to close them and provide a flat surface of sufficient area
+for connection by rivets. Each hollow is separately drained
+by holes with nozzles. Whether this type of trough will
+develop faults of its own, due to over-straining of the metal<span class="pagenum"><a name="Page_28" id="Page_28">[28]</a></span>
+in the act of pressing, remains to be seen; but as it appears
+possible to produce the desired form without any material
+thinning or thickening of the metal, the contention that no
+severe usage accompanies the process appears to be reasonable.</p>
+
+<p>That form of troughing in which the top and bottom
+portions are separately formed, and connected by a horizontal
+seam of rivets at mid-depth, is found in use upon railway
+bridges to be very liable to loosening of those rivets near the
+ends; less surprising, perhaps, because the sloping sides are
+usually thin.</p>
+
+<p>It is a distinctly difficult matter to join two or more
+lengths of any trough flooring having sloping sides, in a
+workmanlike manner; the fit of covers is apt to be imperfect,
+and some rivets, being difficult of access, are likely to be but
+indifferently tight, so that if the joint occurs where it will
+be more than lightly stressed, trouble will probably follow.
+A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most
+severe, any leakage come directly upon the girder, and remedial
+measures be more difficult to carry out.</p>
+
+<p>Timber floors of the best timber, close jointed, are more
+durable than might be supposed. The disadvantage is a
+difficulty in ascertaining the precise condition of the timber
+after many years&#8217; use. The author has seen timbers, 9 inches
+by 9 inches, forming in one length a close floor, carried by
+three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces
+with the foot; whilst in another case, with the same arrangement
+of girders and close-timbered floor, the wood, after
+being in place for thirty-two years, was, when taken out,
+found to be perfectly sound, with the exception of a very
+few bad places of no great extent. In this instance, however,
+it is known that the floor&mdash;pitch-pine&mdash;was put in by a
+contractor who prided himself upon the quality of the timber<span class="pagenum"><a name="Page_29" id="Page_29">[29]</a></span>
+that he used; the floor being also covered with tar concrete,
+which had in this instance so well performed its office as to
+keep the timber quite dry on the top.</p>
+
+<p>Jack arches between girders make an excellent floor for
+road bridges, though heavy; and for small bridges may be
+used to carry rails, if the girders are designed to be stiff under
+load. The apprehension that brickwork or concrete will
+separate from the girder-work, or become broken up under
+even moderate vibration, does not seem to be well founded, if
+the deflection is small and the brickwork or concrete good.</p>
+
+<p>The use of corrugated sheeting as a means of rendering
+the underside of a bridge drop dry cannot be too strongly
+deprecated. If it must be adopted, the arrangement should be
+such as to permit ready removal for inspection and painting.
+It is evident that by boxing up the floor structure, rust is
+favoured, and serious defects may be developed, not to be discovered
+till the sheeting is removed, or something happens.</p>
+
+<div class="figcenter"><a name="Fig20" id="Fig20"></a>
+<p class="caption"><span class="smcap">Fig.</span> 20.</p>
+<img src="images/illo042a.png" alt="" width="600" height="82" />
+</div>
+
+<p>A case may be instanced in which it was found, on taking
+down sheeting of this description, that the floor girders, previously
+hidden, were badly wasted in the webs. One of
+these girders had cracked, as shown in <a href="#Fig20">Fig. 20</a>, and others
+were in a condition only less bad.</p>
+
+<p>In any floor carrying ballast or macadam, if means are
+not adopted to keep the road material from the structure of
+the floor, or from the main girders, corrosion may be serious
+in its effects. Cinder ballast is, perhaps, the worst in this
+respect, in its action upon steel or ironwork, being distinctly
+more damaging than any other kind commonly used.</p>
+
+<p>Rail-joints upon bridge floors are to be avoided where
+practicable by the use of rails as long as can be obtained; if
+the bridge is small enough, crossing it in one length. At
+each joint there is likely to be hammering and working
+extremely detrimental to floor members and connections;
+indeed, it may happen that loose rivets will be found in the<span class="pagenum"><a name="Page_30" id="Page_30">[30]</a></span>
+neighbourhood of such joints, and nowhere else on the bridge.
+Where rail-joints cannot be
+avoided, their position should,
+if there be any choice, be judiciously
+selected, and the plate-layers
+taught to close the joints
+and jam the fish-bolts.</p>
+
+<div class="figcenter"><a name="Fig21" id="Fig21"></a>
+<img src="images/illo042b.png" alt="" width="600" height="108" />
+<p class="caption"><span class="smcap">Fig.</span> 21.</p>
+</div>
+
+<p>As rail-joints upon a bridge
+may injuriously affect the floor,
+so also will a weak floor be
+very trying to the rails. A
+remarkable instance of this has
+come under the writer&#8217;s notice,
+where a bridge (<a href="#Fig21">Fig. 21</a>) of
+three 33-feet spans, having
+outer and centre main girders,
+with cross-girders spaced 3 feet
+apart, resting upon the girder
+flanges, but not attached, and
+carrying two roads, had the permanent-way
+in a very bad state.
+The rails proper, with supplementary
+angle-plates, rested
+direct upon the cross-girders,
+which were decidedly light,
+and the whole floor had much
+&#8220;life&#8221; in it, the ill-effect of
+which was shown in thirteen
+breaks in the angle-plates, in
+each case near their ends,
+generally at holes.</p>
+
+<p>It appears probable that
+severe stresses may be thrown
+upon the parts of a floor,<span class="pagenum"><a name="Page_31" id="Page_31">[31]</a></span>
+whether placed at the level of the bottom booms or of
+the top, by changes of length in the booms due to stress.
+The author has, unfortunately, no direct evidence to offer
+in reference to this, tending either for or against the contention.
+If an unplated floor of cross and longitudinal
+girders of usual arrangement be at the bottom boom of
+a large bridge, as the boom lengthens with the imposition
+of load upon the bridge, all the cross-girders from the
+centre towards the abutments will be curved horizontally,
+the middle portion being restrained by the longitudinals
+from moving bodily with the ends. Each cross-girder
+except that at the centre, if there be one, will thus present
+a figure in plan, concave towards the abutment to which it
+is nearest. This will be accompanied by stressing of the
+connections, and a transfer to the longitudinals of as much
+of the tensile stress properly belonging to the booms as the
+stiffness of the cross-girders may communicate.</p>
+
+<p>This in itself will hardly be considerable, and will be the
+less on account of a slight yielding which may be expected
+at the end connections of each longitudinal; but the effect
+upon the cross-girders by horizontal bending will be much
+marked. If the case be supposed of a 200-feet span in steel
+at ordinary loads and stresses, carrying one line of way, with
+cross-girders 20 feet apart, and having no floor-plates, it may
+be ascertained, neglecting for the moment any slight yielding
+of the longitudinal girder connections, that upon the bridge
+taking its full live load there will be the following approximate
+results: Movement at each end of the end cross-girders
+of <sup>3</sup>&#8260;<sub>10</sub> inch, equivalent to a force of 7<sup>1</sup>&#8260;<sub>2</sub> tons, tending to bend
+them horizontally, and a mean stress on the outer edges of the
+girders, 12 inches wide, of 8 tons per square inch due to
+flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge,<span class="pagenum"><a name="Page_32" id="Page_32">[32]</a></span>
+of <sup>3</sup>&#8260;<sub>4</sub> ton per square inch. Normal elongation of the longitudinal
+girder bottom flanges, and compression of the top, modifies
+the figures unfavourably as to the cross-girder top flange.
+Yielding of the connections named before has been neglected
+in arriving at these stresses. If they are sufficiently accommodating
+to give freely, to a mean extent, as between the
+top and bottom of each joint, of <sup>1</sup>&#8260;<sub>29</sub> inch, these results will
+disappear. It is evident, however, that we cannot rely upon
+good work yielding without the existence of considerable forces
+to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.</p>
+
+<p>The most favourable case has been taken; if now it is
+assumed that the floor has continuous plating, the results
+would seem to be much more astonishing. It will appear on
+this supposition that the boom stresses, instead of being
+taken wholly by the booms, are about equally divided between
+these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which
+for the end cross-girders will approach 40 tons at each
+connection&mdash;considerably more than the vertical reaction
+under normal loads.</p>
+
+<p>Palpably, these conclusions must be greatly modified by
+the yield of longitudinal girder ends, and slip of the floor
+rivets in transverse seams. If these rivets be 3<sup>1</sup>&#8260;<sub>2</sub> inch pitch
+and <sup>3</sup>&#8260;<sub>4</sub> inch in diameter, the stress at each, as estimated, would
+be sufficient to induce shear of about 6 tons per square inch&mdash;more
+than enough to cause &#8220;slip.&#8221; After making this allowance,
+it is still evident there must be very serious forces at
+work about the ends of cross-girders under the conditions supposed,
+probably not less than one half the amounts named, as
+with this reduction the floor rivets should not yield, given
+reasonably good work. It is to be observed that the effect of
+live load only has been introduced, on the presumption that the
+longitudinals and floor-plating have not been riveted up till<span class="pagenum"><a name="Page_33" id="Page_33">[33]</a></span>
+the main girders have been allowed to carry the major part
+of the dead load; but even this cannot always be conceded.
+The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these
+possible effects, either with the object of rendering the communication
+of these forces harmless, or making the floor so
+that it shall take little or no stress from the main booms, by
+arranging joints across the floor specially designed to yield,
+the ends of longitudinals being schemed with the same object.
+Where there is no plating, the case is, perhaps, sufficiently
+provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these
+girders upon the top of the cross-girders, when stretching of
+the bottom flanges of the rail-bearers under load may be
+expected, within a little, to keep pace with the lengthening
+of the main booms.</p>
+
+<p>It would appear that light pressed troughs running across
+the longitudinals would, by yielding in every section, also
+furnish relief, as compared with the rigidity of flat plates.</p>
+
+<p>By placing the floor at a level corresponding to the
+neutral axis of the main girders, the communication of stress
+to the floor may be avoided; but it seldom happens that
+there is so free a choice as to floor height relative to the
+girders. This solution is, therefore, of limited application.</p>
+
+<p>It is obvious that somewhat similar effects must obtain to
+those considered in detail, when the floor structure lies at the
+level of top booms, but with forces of compression from the
+booms to deal with, instead of tension.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_34" id="Page_34">[34]</a></span></p>
+
+<h2>CHAPTER IV.<br />
+<span class="chaptitle">BRACING.</span></h2>
+
+<p>Bracing, whether to strengthen a structure against wind, to
+insure the relative positions of its parts, or for any other
+purpose, cannot be arranged with too great care and regard
+to its possible effects. Forces may be induced which the
+connections will not stand, with loose rivets as a consequence,
+and inefficiency of the bracing itself; or, the connections
+holding good, stresses in the main structure may, perhaps,
+be injuriously altered.</p>
+
+<p>To take a not uncommon case, let us suppose a bridge
+consisting of four main girders placed immediately under
+rails of ordinary gauge, and braced in vertical planes only,
+right across from one outer girder to the other. If the
+roads were loaded always at the same time, nothing objectionable
+would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and
+deflects, the bracing under the six-foot will endeavour to
+communicate some part of this load to the other pair of
+girders. If the bracing is so designed that some correctly
+calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections,
+there will be no harmful consequences; but if not, the
+bracings will most probably work at the ends; this, indeed,
+is what frequently happens. There is one other effect which
+will ensue, if the bracing is wholly efficient; a certain twisting
+movement of the bridge will occur, which increases the
+live load upon the outer girder on the loaded side of the<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span>
+bridge to the extent of 10 per cent., with a corresponding
+lifting force at the outer girder on the unloaded side. These
+amounts are not serious, but wholly dispose of any advantage
+it is conceived will be gained by causing the otherwise idle
+girders to act through the medium of the bracing. In road
+bridges of similar arrangement, over which heavy loads may
+pass on any part of the surface, it is clear that the use of
+bracing between girders should not be taken as justifying
+the assumption that the load is distributed over many girders,
+and correspondingly light sections adopted, unless the effect
+of twisting on the whole bridge is also considered, and justifies
+this view; for, as already stated in the case of the railway
+bridge, the net result may be to increase the girder stresses
+instead of reducing them. Generally, it may be deduced
+that the better plan for railway bridges is to brace the girders
+in pairs, leaving, in the case supposed, no bracing between
+the two middle girders, though there will be no objection to
+connecting these by simple transverse members of no great
+stiffness, to assist in checking lateral vibration. For road
+bridges of more than five longitudinal girders, equally spaced,
+it may be advantageous to brace right across, the twisting
+effect with this, or a greater, number of girders not, as a rule,
+leading to any increase of load on any girder. <a href="#Fig22">Figs. 22</a> to
+<a href="#Fig25">25</a> give the distribution of live load, placed as shown, for 3,
+4, 5, and 6 girders.</p>
+
+<p>It is to be observed that these statements do not apply to
+cases where there may be also a complete system of horizontal
+bracing, the effect of which, in conjunction with cross
+diagonals, may be greatly different, with considerable forces
+set up in the bracing, and a modification of girder stresses.</p>
+
+<p>These effects may be so considerable as to call for special
+attention in design where such an arrangement is adopted.</p>
+
+<div class="figc600"><a name="Fig22" id="Fig22"></a><a name="Fig23" id="Fig23"></a><a name="Fig24" id="Fig24"></a><a name="Fig25" id="Fig25"></a>
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 22.</span> <span class="right60"><span class="smcap">Fig.</span> 24.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 22. and <span class="smcap">Fig.</span> 24.</p>
+
+<img src="images/illo048.png" alt="" width="600" height="235" />
+<p class="caption_b"><span class="left39"><span class="smcap">Fig.</span> 23.</span> <span class="right60"><span class="smcap">Fig.</span> 25.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 23. and <span class="smcap">Fig.</span> 25.</p>
+</div>
+
+<p>Somewhat similar straining to that first indicated may
+occur in bracings placed between the girders of a bridge<span class="pagenum"><a name="Page_36" id="Page_36">[36]</a></span>
+much on the skew. If this is, on plan, at right angles to
+the girders, as is commonly and properly the case, the ends
+will evidently be attached to the girders at points on their
+length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts,
+and the bracing will, if at one end attached near a rigid
+bearing, transfer some part of the load from one girder to<span class="pagenum"><a name="Page_37" id="Page_37">[37]</a></span>
+the other, notwithstanding that both girders may be of the
+same span and equal extraneous loading. It would not be
+difficult to ascertain the amount of load so transferred from
+a consideration of the relative movements if free, and the
+loads on the two girders necessary to render these movements
+equal, if the deflections were simply vertical; but as there
+will be some twisting and yielding of the girders on their
+seats, the calculation becomes involved. If the bracing is
+placed at about the middle of the girders, the effects noted
+will be greatly reduced; first, because the difference of
+movements near the centre will be less; second, any given
+difference will correspond to a smaller transference of load;
+and, third, because each girder will there be more free to
+twist than at the ends. It therefore appears that bracings
+between the girders of a skew bridge should not be placed
+near the bearings, though they may be put, with much less
+risk of injury, near the middle.</p>
+
+<p>Cross-girders on a skew bridge are subject to forces
+somewhat similar to those which may affect bracing, rendering
+it desirable to design their attachments in a manner
+which shall not aggravate the matter, but rather reduce the
+effects of unequal vertical displacement of their ends where
+secured to the main girders.</p>
+
+<p>Crossed flat bars as bracing members are objectionable
+on account of their tendency to rattle, after working loose;
+but as this effect only ensues in bracing which has first
+become loose (it being assumed that the bars in any case are
+connected where they cross), this objection is not itself vital,
+though greater rigidity is easily obtained by making all such
+members of a stiff section.</p>
+
+<p>Defective bracing between girders, from neglect of the
+very considerable forces it may be called upon to communicate,
+is very common; the writer has seen many such cases,
+of which one is here illustrated in <a href="#Fig26">Fig. 26</a>.</p>
+
+<p><span class="pagenum"><a name="Page_38" id="Page_38">[38]</a></span></p>
+
+<div class="figcenter"><a name="Fig26" id="Fig26"></a>
+<img src="images/illo050.png" alt="" width="600" height="298" />
+<p class="caption"><span class="smcap">Fig.</span> 26.</p>
+</div>
+
+<p>This bridge, of the section shown, and 85 feet span, had
+very light web structure. The bracings, of which there
+were two sets, were wholly inefficient, the end rivets being
+loose in enlarged holes. Upon the passage of a train there
+was a positive lurching of the girder tops from side to side.<span class="pagenum"><a name="Page_39" id="Page_39">[39]</a></span>
+The integrity of the bridge was really dependent upon such
+stiffness as there was in the girders, and unplated floor.</p>
+
+<p>A common but indifferent method of keeping the top
+members of main girders in line is by the use of overhead
+girders alone, frequently curved to give the requisite clearance
+over the road. This cannot be considered as wholly
+inefficient, as sometimes maintained, since it is evident that
+the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must
+take a greater force to distort it than would be necessary to
+cause deformation of a corresponding degree, in an open
+frame formed by the omission of the overhead girder; but it
+is not a method to be recommended, its precise utility is
+difficult to estimate, and, if the cross-girder attachments are
+of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however,
+not applicable to this arrangement alone. All overhead
+bracing favours this by restraining the tendency of the top
+booms to cant inwards when the floor beams are loaded; and
+though this restraint may be quite harmless, it is desirable
+that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in
+its character. &#8220;Sway&#8221; bracing, sometimes introduced at
+right angles to the bridge between opposite verticals, tends
+to emphasise these effects by rendering the cross-section of
+the bridge still stiffer, besides making it a matter of difficulty
+to ascertain how much of the wind forces on the top boom
+is carried to the abutment by the top system of bracing, and
+how much by the floor. The author does not, however, mean
+to suggest that it cannot be used with propriety, but rather
+that extreme care is desirable in considering its ultimate
+effect on the rest of the structure.</p>
+
+<p>For girders of moderate depth there may be on these
+grounds a distinct advantage in abandoning overhead bracing,<span class="pagenum"><a name="Page_40" id="Page_40">[40]</a></span>
+and securing rigidity of the top boom, and adequate
+resistance to wind forces, by making the connection between
+the cross-girders and the web members sufficiently good to
+insure, as a whole, a stiff <span class="lettsymb">U</span>-shaped frame; but this, with
+the ordinary type of rocker arrangement under the main
+girder bearings, will not be entirely free from objection, as
+canting of the girders due to floor loading will throw extreme
+pressure on the inner end of each rocker. There appears to
+be no reason why the cylindrical knuckle should not in this
+case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.</p>
+
+<div class="figcenter"><a name="Fig27" id="Fig27"></a>
+<img src="images/illo053.png" alt="" width="300" height="357" />
+<p class="caption"><span class="smcap">Fig.</span> 27.</p>
+</div>
+
+<p>The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom
+flanges, renders very narrow top booms permissible. This is
+a decided advantage where lightness of appearance is aimed
+at; but it is not unusual to see an attempt made in this
+direction by introducing gusset plates of very ample proportions
+between vertical members of the girders, and the projecting
+ends of flimsy transoms, carried beyond the width of
+the bridge proper, these being of a section wholly out of
+proportion to the brackets they are supposed to secure.
+Whatever may be the amount of strength necessary at the
+point A, in <a href="#Fig27">Fig. 27</a>, there should not be less throughout the
+transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the
+vertical stiffeners is not, as a rule, great. Information to
+enable this question to be dealt with as a matter of calculation
+is somewhat scanty; but it would appear to be sufficient
+to insure safety that, for an assumed small amount of curvature
+in the compression member, the forces outwards corresponding
+to this curvature, due to thrust, should be resisted
+by verticals and transoms of strength and stiffness sufficient
+to restrain it from any further flexure. It will, of course,
+be necessary also to take care that the compression member<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span>
+is good as a strut between the points of restraint. A
+simple and sufficiently precise method of dealing with this
+question is much needed. In cases where the floor weight
+rests on the flange projection, it is also necessary to give
+the transom additional strength to an extent enabling it
+to resist the twisting effort between any two of these
+transverse members; further, resistance to wind on the
+girder has to be provided in both transoms and verticals.</p>
+
+<p>It may be hardly
+necessary to insist
+that bracing intended
+to stiffen a structure
+against wind, local
+crippling, or vibration,
+should be made
+complete, not stopping
+short at some
+point, because it cannot
+conveniently be
+carried further, as
+is sometimes done,
+unless the strength
+of those parts of
+the structure through
+which the forces from
+the bracing must be communicated to the abutments is
+sufficiently great, considered with reference to other stresses
+in those parts which have also to be endured.</p>
+
+<p>Bracing stopped short in this way, making only the
+central part of a bridge rigid, may have the effect of increasing
+the forces to which the unstiffened end members would
+otherwise be liable. Such a structure would evidently be
+much stiffer against wind-gusts than if no bracing existed&mdash;the
+resistance to a blow would be increased; but the power to<span class="pagenum"><a name="Page_42" id="Page_42">[42]</a></span>
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater
+maximum forces than if bracing were wholly omitted. The
+net effect may still be better than with no bracing, the point
+raised being simply that of an increase of stress in particular
+end members.</p>
+
+<p>In the bracing of tall piers, the rising members of which
+will be subject to any considerable stress, if the diagonal
+members are not finally secured when the piers are under
+their full load, or an initial stress of proper amount induced
+in those members, the effect of loading will be to render
+them slack; so that an appreciable amount of movement at
+the top may occur before it can be limited by the efficient
+action of the bracings. This effect under blasts of wind or
+continual passage of trains may, indeed, be dangerous.
+Similar considerations apply to the top wind bracing of deep
+girder bridges, influencing also the bottom bracing in a contrary
+manner, which calls for attention in fixing the unit
+stresses for such members.</p>
+
+<p>The bracing of sea-piers is very liable to slacken if made
+with pin-and-eye ends, as is often done for round rods. The
+detail presents advantages in erection, but is not altogether
+satisfactory in practice. Such connections are continually
+working. In the finest weather, with the sea quite smooth
+but for an almost imperceptible wave movement, the lower
+parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there
+room for surprise when it is considered that these oscillations,
+occurring at about ten to each minute, never wholly cease,
+and amount in the course of one year to over five million in
+number.</p>
+
+<p>Bracing attached in such a manner that there can be no
+initial slack, or slack due to wear under endless repetitions
+of small amounts of stress, will have a much better chance to<span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span>
+keep tight. The advantage presented by round rods in
+offering little surface to the water, is more than negatived
+by inefficiency of the usual attachments for such rods.</p>
+
+<p>The author has observed that bracing of members possessing
+some stiffness, and with good end attachments to ample
+surfaces, appears to stand best in ordinary sea-pier work.
+For such structures the bracing should consist of a few
+good members, with a solid form of attachment, rather than
+of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very
+possibly also, in the case of sea-pier work, in unskilled hands.
+If round rods must be used, they will stand much better if
+made of large diameter.</p>
+
+<p>Before leaving the subject of bracing, it may not be out
+of place to refer to wind pressure, as this may so much affect
+the proportioning of the members.</p>
+
+<p>Some years since the author had occasion to examine a
+number of structures with respect to their stability. Of foot-bridges
+from 60 feet to 120 feet long, three or four, when
+calculated on the basis recommended by the Board of Trade
+as to pressures upon open-work structures, worked out at an
+overturning pressure of from 18 lb. to 22 lb. per square foot.
+These bridges had been many years in existence; it is,
+therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them
+as to the whole surface.</p>
+
+<div class="figcenter"><a name="Fig28" id="Fig28"></a>
+<img src="images/illo056.png" alt="" width="400" height="333" />
+<p class="caption"><span class="smcap">Fig.</span> 28.</p>
+</div>
+
+<p>Particulars were taken in 1895 of a notice-board, presenting
+about 12 square feet of surface, which was blown down
+in the great storm of March 24 of that year, at Bilston, in
+Staffordshire. It was situated at the foot of a slight slope,
+over which the wind came, striking the obstruction at right
+angles. The board was mounted on two oak posts of fair
+quality and condition, which broke near the ground at bolt
+holes (see <a href="#Fig28">Fig. 28</a>). The force required to do this, at 9000 lb.<span class="pagenum"><a name="Page_44" id="Page_44">[44]</a></span>
+modulus of rupture&mdash;a moderate value&mdash;corresponds to 50 lb.
+per square foot on the surface exposed above the break.</p>
+
+<p>In the same neighbourhood, at the same time, considerable
+damage was wrought in overturning chimney stacks, to
+buildings and roofs; the general impression in the locality
+being that the storm was of exceptional, even unprecedented,
+violence. Bilston, it should be noted, lies high.</p>
+
+<p>At Bidston Hill, near Birkenhead, on the same occasion,
+a pressure of 27 lb. was registered. In another part of the
+country it is said to have been 37 lb. Wind is so capricious
+in its effects over small areas as to render it probable that the
+maximum pressures have never been recorded; but this is
+a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by
+themselves insufficient to throw much light on the question,
+may be of use in connection with other known examples.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span></p>
+
+<h2>CHAPTER V.<br />
+<span class="chaptitle">RIVETED CONNECTIONS.</span></h2>
+
+<p>Considerable latitude is observable in the practice of
+engineers in the use of rivets. Numberless experiments to
+determine the resistance of riveted connections have from
+time to time been made, but these are not to be considered
+by themselves as final, when the results of experience in
+actual construction, are available for further enlightenment.</p>
+
+<p>The class of workmanship so largely influences the degree
+in which rivets will maintain their integrity that it is only
+by the observation of a large number of cases, including all
+degrees of workmanship, that any reliable conclusions may
+be drawn. In this respect laboratory experiments have an
+apparent advantage, as the conditions may be kept sensibly
+the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must
+in the end determine the utility of any inquiry for practical
+application.</p>
+
+<p>The author has studied the particulars of a number of
+cases to ascertain under what conditions as to stress, having
+due regard to the effects of vibration, rivets will remain tight,
+or become loose. Every loose rivet that may be found cannot,
+of course, be taken as being due to excessive stress; the more
+frequent cause is indifferent work, evidenced by the fact that
+neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon
+the remainder. When rivets loosen as the direct result of
+over-stress, it is usually by compression of the shank and<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span>
+enlargement of the hole, or by stretching of the rivet and
+reduction of its diameter. Instances of failure by partial or
+complete shear are extremely rare; indeed, the author has
+never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work,
+it is not uncommon to find it cut or bent as an after consequence.</p>
+
+<p>In estimating stresses at which rivets have remained
+tight, or loosened, as the case may be, examples have generally
+been chosen in which there could be no reasonable
+doubt as to the amount of those stresses by the ordinary
+methods of computation. This is clearly most important,
+as, if any appreciable uncertainty remained as to the degree
+of stress, the results deduced would be of little value. For
+this reason those instances in which the loads upon girders,
+or parts of girders, may find their way to the supports by
+more than one route, are to be regarded with caution, as are
+those in which full loading possibly never obtains, but which
+may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been
+used in making the computations; in some cases from
+direct measurement from particular rivets, in others with a
+suitable allowance for excess diameter of hole, according to
+the class of work under consideration.</p>
+
+<p>Dealing first with main girders, it may be said that rivets
+attaching the webs of plate girders to the flange angles rarely
+loosen, though subject to considerable stress. In illustration
+of this may be named a bridge for two lines of way, 85 feet
+effective span, having two main girders with plate webs, and
+cross-girders resting on the top flanges, previously referred
+to (see <a href="#Fig26">Fig. 26</a>).</p>
+
+<p>The girders, which were 6 feet 9 inches deep, had a bearing
+upon the abutments of 4 feet; the rivets were <sup>7</sup>&#8260;<sub>8</sub> inch in
+diameter and 4 inches pitch. There is in a case of this kind<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span>
+some little uncertainty as to what is the stress on the flange
+angle rivets at, or very near to, the bearings; but, taking
+the vertical rows of rivets at the web joints near the ends as
+presenting less uncertainty, the stress per rivet works out at
+4&middot;8 tons, being 4 tons per square inch on each shear surface,
+and 11 tons per square inch bearing pressure upon the shank
+in the web plate, which was barely <sup>1</sup>&#8260;<sub>2</sub> inch thick. This bridge
+was frequently loaded upon both roads, but with one road
+only carrying live load, the stresses in the more heavily
+loaded girder would be fully 90 per cent. of those obtaining
+as a maximum. There was on this bridge, which had been
+in use 31 years, considerable movement and vibration.</p>
+
+<p>It is by no means uncommon to find cases of rivets in
+main girders taking 11 tons per square inch bearing pressure&mdash;occasionally
+more&mdash;and remaining tight. As furnishing
+an instructive, though slightly ambiguous, instance of rivets
+in single shear, may be cited a bridge not greatly less than
+that just referred to, of about 65 feet span, carrying two
+lines of way, there being two outer and one centre main
+girder of multiple lattice type, with cross-girders in one
+length 4 feet apart, riveted to the bottom booms of the main
+girders; these rivets, by the way, were in tension. The
+floor was plated, the road consisting of stout timber longitudinals,
+chairs, and rails (<a href="#Fig29">Fig. 29</a>).</p>
+
+<div class="figcenter"><a name="Fig29" id="Fig29"></a>
+<img src="images/illo060.png" alt="" width="600" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 29.</p>
+</div>
+
+<p>It should be noted that there is in this case some difficulty
+in ascertaining the precise behaviour of the cross-girders,
+affecting the proportion of load carried by the outer
+and the inner main girders. Strict continuity of all the
+cross-girders could only obtain if the deflection of the main
+girders were such as to keep the three points of suspension of
+each cross-girder in the same straight line. A close inquiry
+showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would,
+under load, by relative depression of the middle point of<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span>
+support, be reduced to the condition of two simple beams,
+those at the extreme ends of the span would behave as
+continuous girders.</p>
+
+<p>With both roads carrying
+engine loads equal to those
+coming upon the bridge, the
+author estimates that for the
+centre main girder the shear
+on the rivets of the end diagonals,
+secured by one rivet
+only, was 14&middot;9 tons per square
+inch, and the bearing pressure
+16&middot;3 tons; the flange stress
+being 7&middot;1 tons per square inch
+net. The outer main girders
+are most heavily stressed when
+but one road, next to the
+outer girder considered, carries
+live load. For this condition
+the stresses work out at
+9 tons per square inch shear
+on the rivets of the end diagonals,
+and 9 tons bearing
+pressure, the flange stress being
+5&middot;7 tons per square inch
+on the net section.</p>
+
+<p>Without intending to
+throw any doubt upon the
+substantial truth of these
+results, it must be admitted
+that instances of greater simplicity
+of stress determination
+are much to be preferred. For purposes of comparison, but
+not as having any other value, the results have also been<span class="pagenum"><a name="Page_49" id="Page_49">[49]</a></span>
+worked out on the supposition of all cross-girders acting
+each as two simple beams, and also for strict continuity, and
+are here tabulated, together with the conclusions given above.</p>
+
+<p>The cross-girders were moderately stressed, and the tension
+on the rivets attaching them to the main girders
+probably did not exceed 3 tons per square inch.</p>
+
+<p>It should be pointed out that the traffic over the bridge
+was small. The centre main girder but seldom bore its full
+load, though at all times liable to receive it. Much importance
+cannot, therefore, be attached to the results for this
+girder, other than as showing how a structure may stand for
+many years, though liable at any time to the development
+of stresses which would commonly be regarded as destructive,
+or nearly so.</p>
+
+<p class="center"><span class="smcap">Examples of Rivet Stresses, etc., in Lattice Girders.</span></p>
+
+<table class="nowrap" summary="Table page 49">
+
+<tr class="bt bb">
+<th rowspan="2" class="br">&mdash;</th>
+<th class="br">Cross-<br />Girders<br />as Simple<br />Beams.</th>
+<th class="br">Cross-<br />Girders<br />as Con-<br />tinuous<br />Beams.</th>
+<th>Correct<br />Results.</th>
+</tr>
+
+<tr class="bb">
+<th colspan="3">Stress in Tons per Square Inch.</th>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Centre girder, 63 ft. span (both roads loaded):</td>
+<td class="br">&nbsp;</td>
+<td class="br">&nbsp;</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">Rivets in diagonals&mdash;Shear</td>
+<td class="right padl1 padr2 br">13&middot;7</td>
+<td class="right padl1 padr2 br">17&middot;2</td>
+<td class="right padl1 padr2">14&middot;9</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals&mdash;</span><span class="padl0">Bearing pressure</span></td>
+<td class="right padl1 padr2 br">15&middot;0</td>
+<td class="right padl1 padr2 br">18&middot;8</td>
+<td class="right padl1 padr2">16&middot;3</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals&mdash;</span><span class="padl0">Flange stress</span></td>
+<td class="right padl1 padr2 br">6&middot;8</td>
+<td class="right padl1 padr2 br">8&middot;5</td>
+<td class="right padl1 padr2">7&middot;1</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br blankabove">Outer girder, 66 ft. span (near road loaded):</td>
+<td class="br blankabove">&nbsp;</td>
+<td class="br blankabove">&nbsp;</td>
+<td class=" blankabove">&nbsp;</td>
+</tr>
+
+
+<tr>
+<td class="padl3 padr1 br">Rivets in diagonals&mdash;Shear</td>
+<td class="right padl1 padr2 br">9&middot;6</td>
+<td class="right padl1 padr2 br">8&middot;2</td>
+<td class="right padl1 padr2">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="padl3 padr1 br"><span class="noshow">Rivet</span>Do.<span class="noshow">diagonals&mdash;</span><span class="padl0">Bearing pressure</span></td>
+<td class="right padl1 padr2 br">9&middot;6</td>
+<td class="right padl1 padr2 br">8&middot;2</td>
+<td class="right padl1 padr2">9&middot;0</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl3 padr1 br"><span class="noshow">Rivets in diagonals&mdash;</span><span class="padl0">Flange stress</span></td>
+<td class="right padl1 padr2 br">5&middot;9</td>
+<td class="right padl1 padr2 br">5&middot;1</td>
+<td class="right padl1 padr2">5&middot;7</td>
+</tr>
+
+</table>
+
+<p>The material and workmanship of the bridge were good.
+The rivets of the centre girder end diagonals, 1 inch in
+diameter, were originally <sup>7</sup>&#8260;<sub>8</sub> inch, but on becoming loose were<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span>
+cut out, the holes reamered, and replaced by the larger size,
+which remained tight, and to which the stress figures apply.
+The rivets in the diagonals near the centre, <sup>7</sup>&#8260;<sub>8</sub> inch in diameter,
+which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The
+riveting in the outer girder diagonals, subject to smaller
+stresses, much more frequently developed, also gave trouble,
+particularly those liable to counter stresses.</p>
+
+<p>Apart from looseness of rivets, the general appearance
+and behaviour of the bridge, which had been in existence
+about twenty years, was not suggestive of any weakness.</p>
+
+<p>Of smaller girders, an example showing the necessity for
+care in discriminating, if it be possible, between looseness
+of rivets resulting from over-stress and that due to other
+influences may first be quoted. Two trough girders, of
+11 feet effective span, each of the section shown in <a href="#Fig30">Fig. 30</a>,
+11<sup>1</sup>&#8260;<sub>2</sub> inches deep at the ends, 14 inches at the middle, with
+<sup>1</sup>&#8260;<sub>4</sub>-inch webs, and rivets <sup>3</sup>&#8260;<sub>4</sub> inch in diameter, of 4<sup>1</sup>&#8260;<sub>2</sub>-inch pitch,
+showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (<a href="#Fig31">Fig. 31</a>). From the nature
+of the arrangement the lower web rivets, which were loose,
+would receive the first shock of the load coming upon the
+span, but there were evidences indicative of original bad
+work. The angle bars gaped, suggesting that these had
+first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets
+failing to pull the work close, and then readily working loose.
+Here there is considerable uncertainty as to how much of
+the loosening is to be attributed to bad work, and how much
+to stress. It may, however, be remarked that whatever
+bearing stress was the ultimate result of the load hammering
+on the lower angle flanges, loosening rivets never perhaps
+really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable<span class="pagenum"><a name="Page_51" id="Page_51">[51]</a></span>
+impactive force, was not sufficient to loosen these. The
+girders were taken out after being in place sixteen years.</p>
+
+<div class="figc600"><a name="Fig30" id="Fig30"></a><a name="Fig31" id="Fig31"></a><a name="Fig32" id="Fig32"></a>
+<p class="caption_b"><span class="left53"><span class="smcap">Fig.</span> 30.</span> <span class="right46"><span class="smcap">Fig.</span> 32.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 30. and <span class="smcap">Fig.</span> 32.</p>
+<img src="images/illo063.png" alt="" width="600" height="320" />
+<p class="caption"><span class="smcap">Fig.</span> 31.</p>
+</div>
+
+<p>An instance of undoubted excessive bearing pressure
+was found in the cross-girders of a bridge, mentioned on
+<a href="#Page_15">p. 15</a>, of which so many web plates were cracked. This
+bridge, carrying two lines of way, had outer main girders,
+and long cross-girders with <sup>1</sup>&#8260;<sub>4</sub>-inch webs and <sup>3</sup>&#8260;<sub>4</sub>-inch rivets,<span class="pagenum"><a name="Page_52" id="Page_52">[52]</a></span>
+4 inches pitch. The rivet stresses work out at 4&middot;3 tons per
+square inch on each shear surface, and 24 tons per square
+inch bearing pressure. For
+one road only being loaded, the
+latter figure falls to 18&middot;5 tons.
+The traffic over this bridge,
+twenty years old, was considerable,
+rapid, and heavy. It is
+hardly necessary to add that
+a large number of the rivets
+were loose, one of which is
+shown in <a href="#Fig32">Fig. 32</a>.</p>
+
+<div class="figcenter"><a name="Fig33" id="Fig33"></a>
+<img src="images/illo064.png" alt="" width="600" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 33.</p>
+</div>
+
+<p>To take another case relating
+to a floor system of extremely
+bad design (<a href="#Fig33">Fig. 33</a>).
+The main girders were 11 feet
+apart, 35 feet span, the floor
+having two cross-girders only,
+spaced at 11 feet 3 inches, and
+9 inches deep, supporting hog-backed
+trough longitudinals.
+The cross-girders were at their
+ends but 6<sup>3</sup>&#8260;<sub>4</sub> inches deep, the
+distance from the bearing of
+cross-girders to centre of longitudinals
+carrying a rail being
+2 feet 10 inches, in which
+length were eight rivets in the
+web and angles at the top, and
+six at the bottom, all <sup>3</sup>&#8260;<sub>4</sub> inch in
+diameter.</p>
+
+<p>The shear stress on the upper rivets works out at 7&middot;3
+tons per square inch on each shear surface, the bearing pressure
+20&middot;6 tons per square inch. On the lower rivets the<span class="pagenum"><a name="Page_53" id="Page_53">[53]</a></span>
+shear stress becomes 9&middot;7 tons, and the bearing pressure
+27&middot;4 tons, per square inch. Care was exercised in computing
+these stresses, that part of the bending moment
+carried by the web being allowed for, but it must be admitted
+that the result is, probably, approximate only. The <a href="#Fig33">sketch</a>
+here given shows the cross-girder end and section. The
+rivets, though in double shear, were, as might be expected,
+loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled
+after twelve years&#8217; use.</p>
+
+<p>In illustration of the behaviour of rivets in the ends of
+long cross-girders, both shallow and weak, and many years
+in use under heavy traffic, may be cited connections having
+end angle bars to the cross-girders, with six rivets through
+the web of main girders. The bearing pressure worked out
+at 7&middot;8 tons per square inch. Many rivets were loose, but it
+should be remarked that the workmanship was not of the
+best class, and the cross girders flexible: a characteristic
+very trying to end rivets, and inducing a stretch in some,
+already referred to as a possible cause of loosening. This
+will be apparent if the probable end slope of weak girders
+be considered. The author concludes that this inclination
+should not, for ordinary cases, exceed 1 in 250; but the
+ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly
+regarded as bad practice to submit rivets to tension, yet this
+is frequently, though unintentionally, permitted in end attachments,
+without any attempt to limit the amount of
+tension. With suitable restrictions, there appears no serious
+objection to rivet tension for many situations.</p>
+
+<p>Another instance of cross-girder end connections of a
+different type is illustrated in <a href="#Fig34">Fig. 34</a>.</p>
+
+<div class="figcenter"><a name="Fig34" id="Fig34"></a>
+<img src="images/illo066a.png" alt="" width="300" height="328" />
+<p class="caption"><span class="smcap">Fig.</span> 34.</p>
+</div>
+
+<p>The main girders of the bridge were 12 feet apart, each
+cross-girder end carrying its share of the half of one road.<span class="pagenum"><a name="Page_54" id="Page_54">[54]</a></span>
+The mean bearing pressure upon the rivet shanks works out
+at 5&middot;8 tons per square inch for the six rivets of the original
+joint, but in the particular joint shown some of the rivets
+had loosened, making the bearing pressure upon the remainder
+about 8&middot;7 tons per square inch. It is apparent
+there must have been considerable stress on the top and
+bottom rivets which loosened. These two rivets would also,
+because of difficult access, be in all likelihood insufficiently
+hammered up. The joints worked rather badly; the loose
+rivets had &#8220;cut&#8221; to a considerable extent, a process materially
+assisted by the gritty nature of the ballast (limestone),
+particles of which, getting into the joint, contributed to the
+sawing action; this had clearly been taking effect for some
+considerable time. (See <a href="#Fig35">Fig. 35</a>.)</p>
+
+<div class="figcenter"><a name="Fig35" id="Fig35"></a>
+<img src="images/illo066b.png" alt="" width="350" height="219" />
+<p class="caption"><span class="smcap">Fig.</span> 35.</p>
+</div>
+
+<p>The two cases of cross-girder ends given are both rather
+exceptional in character, and in each case the defects appear
+to be due to general bad design and workmanship rather
+than to any serious excess of bearing pressure. This may
+be illustrated by taking the common case of cross-girders,
+2 feet deep, carrying two roads, and having end angle irons
+riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span>
+is, for old work, simply typical, and does not relate to any
+specific instance, the bearing pressure on the rivets will work
+out at from 6 to 8 tons per square inch, and will seldom be
+accompanied by looseness of rivets, and then only as a result
+of faulty work.</p>
+
+<p>Some sketches of rivets taken from old bridges have
+already been given in connection with the cases to which
+they belong; a few others are here shown (<a href="#Fig36">Figs. 36</a> to <a href="#Fig40">40</a>)
+to further illustrate what may be the actual condition of
+rivets after some years&#8217; use, and how different from the ideal
+rivet upon which calculations are based. These are, however,
+bad instances.</p>
+
+<div class="figc350"><a name="Fig36" id="Fig36"></a><a name="Fig37" id="Fig37"></a>
+<img src="images/illo067a.png" alt="" width="350" height="88" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 36.</span> <span class="right49"><span class="smcap">Fig.</span> 37.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 36. and <span class="smcap">Fig.</span> 37.</p>
+</div>
+
+<div class="figc350"><a name="Fig38" id="Fig38"></a><a name="Fig39" id="Fig39"></a>
+<img src="images/illo067b.png" alt="" width="350" height="81" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 38.</span> <span class="right49"><span class="smcap">Fig.</span> 39.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 38. and <span class="smcap">Fig.</span> 39.</p>
+</div>
+
+<div class="figcenter"><a name="Fig40" id="Fig40"></a>
+<img src="images/illo067c.png" alt="" width="150" height="84" />
+<p class="caption"><span class="smcap">Fig.</span> 40.</p>
+</div>
+
+<p>It should be noticed that rivets may, if in double shear,
+be loose in the middle thickness, due to enlargement of the
+hole in the central part and compression of the rivet, and
+yet show no sign of this by testing with the hammer. There
+is, however, generally marked evidence of another kind in<span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span>
+the &#8220;working&#8221; of the inner part, as, for instance, the web
+of a plate girder, in which case a discoloration due to rust is
+to be found along the edges of the angle bars, or a movement
+may be detected on the passage of live load. Red rust is, in
+fact, frequently an indication of something wrong, when no
+other evidence is apparent. In plate girders having <span class="lettsymb">T</span> or <span class="lettsymb">L</span>
+bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching
+these bars to the cross-girder tops loose, due to causes already
+dealt with. The riveted connection should, as to strength,
+bear some relation to the strength and stiffness of the parts
+secured, if the rivets are to remain sound.</p>
+
+<p>It may be well to give here a summarised statement of
+the results already named, for purposes of ready reference.
+These by themselves are not sufficient to enable working
+stresses to be deduced, though they are instructive. The<span class="pagenum"><a name="Page_57" id="Page_57">[57]</a></span>
+author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which
+the rivets behaved well, but is not now able to give precise
+particulars of these.</p>
+
+<p class="center"><span class="smcap">Examples of Rivet Stresses.</span></p>
+
+<table class="nowrap" summary="Table page 56">
+
+<tr class="bt bb">
+<th colspan="4" class="center br">&mdash;</th>
+<th class="center padl1 padr1 br">Span<br />in<br />Feet.</th>
+<th class="center padl1 padr1 br">Where<br />Found.</th>
+<th class="center padl1 padr1 br">Shear<br />Stress<br />in Tons<br />per<br />Square<br />Inch.</th>
+<th class="center padl1 padr1 br">Single<br />or<br />Double<br />Shear.</th>
+<th colspan="3" class="center padl1 padr1 br">Bearing<br />Pressure<br />in Tons<br />per<br />Square<br />Inch.</th>
+<th colspan="4" class="center padl1 padr1">Tight<br />or<br />Loose.</th>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="3" class="left padl1 padr1">Main girders</td>
+<td rowspan="3" class="right padr0 narrow">-</td>
+<td rowspan="3" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="3" class="narrow br">&nbsp;</td>
+<td class="center padl1 padr1 br">85</td>
+<td class="center padl1 padr1 br">Web</td>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="center padl1 padr1 br">D</td>
+<td rowspan="3" colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">11&middot;0</td>
+<td rowspan="3" colspan="3">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">66</td>
+<td class="center padl1 padr1 br">Diagonals</td>
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="center padl1 padr1 br">S</td>
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">63</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr2 br">14&middot;9</td>
+<td class="center padl1 padr1 br">S</td>
+<td class="right padl1 padr2 br">16&middot;3</td>
+<td class="left padr1">Tight generally.</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="4" class="left padl1 padr1">Small girders</td>
+<td rowspan="4" class="right padr0 narrow">-</td>
+<td rowspan="4" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="4" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">11</td>
+<td class="center padl1 padr1 br">Web</td>
+<td class="right padl1 padr2 br">1&middot;4</td>
+<td class="center padl1 padr1 br">D</td>
+<td rowspan="4" colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td rowspan="4" colspan="3" class="narrow">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">26</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">4&middot;3</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">24&middot;0</td>
+<td class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">11</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">7&middot;3</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">20&middot;6</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">11</td>
+<td class="center br">&#8222;</td>
+<td class="right padl2 padr1 br">9&middot;7</td>
+<td class="center padl1 padr1 br">D</td>
+<td class="right padl1 padr2 br">27&middot;4</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr>
+<td rowspan="3" class="left padl1 padr1">End connections</td>
+<td rowspan="3" class="right padr0 narrow">-</td>
+<td rowspan="3" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="3" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">27</td>
+<td class="center padl1 padr1 br">Ends</td>
+<td class="right padl1 padr2 br">5&middot;4</td>
+<td class="center padl1 padr1 br">S</td>
+<td colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;8</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Loose.</td>
+</tr>
+
+<tr>
+<td rowspan="2" class="center padl1 padr1 br">12</td>
+<td rowspan="2" class="center br">&#8222;</td>
+<td rowspan="2" class="right padl1 padr2 br">1&middot;8</td>
+<td rowspan="2" class="center padl1 padr1 br">D</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td class="right padl1 padr2 br">5&middot;8</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1">Many loose.</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">8&middot;7</td>
+</tr>
+
+<tr>
+<td colspan="4" class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td class="thinrow br">&nbsp;</td>
+<td colspan="3" class="thinrow br">&nbsp;</td>
+<td colspan="4" class="thinrow">&nbsp;</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl1 padr1">(Type case)</td>
+<td colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">26</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr2 br">4&middot;8</td>
+<td class="center padl1 padr1 br">S</td>
+<td colspan="2">&nbsp;</td>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Tight.</td>
+</tr>
+
+</table>
+
+<p>It is probable that the fact of a rivet being in single or
+in double shear largely affects its ability to resist the effects
+of bearing pressure, as commonly estimated. In the first
+case, the rivet-shank must bear heavily on the half-thickness
+of the plates or bars through which it passes, rather than on
+the whole thickness; and it is to be supposed that under
+this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.</p>
+
+<div class="figc400"><a name="Fig41" id="Fig41"></a><a name="Fig42" id="Fig42"></a>
+<img src="images/illo069.png" alt="" width="400" height="183" />
+<p class="caption_b"><span class="left43"><span class="smcap">Fig.</span> 41.</span> <span class="right56"><span class="smcap">Fig.</span> 42.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 41. and <span class="smcap">Fig.</span> 42.</p>
+</div>
+
+<p>The author has no very definite information in
+support of this contention, but suggests that for double
+shear the permissible bearing pressure may probably be as
+much as 50 per cent. greater than for rivets in single shear;
+the difference being made rather in the direction of increasing
+the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this
+is evident when it is considered that the practice has commonly
+been to make no distinction, so that whatever bearing
+pressures are found to be sufficient for both cases may be
+increased for those capable of taking the greater amount.
+<a href="#Fig41">Figs. 41</a> and <a href="#Fig42">42</a>, here given, illustrate the behaviour of rivets
+under the two conditions.</p>
+
+<p><span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span></p>
+
+<p>With reference to the amounts of the stresses to which
+rivets may be subject, the author concludes, as a result of his
+experience, coupled with a consideration of known laboratory
+tests, that for all dead load these may be quite prudently
+higher than is frequently taken. For iron the shear stress
+to be 10 per cent. less than the stress of parts joined; and
+the bearing pressure&mdash;for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary
+mild steel the shear stress to be 20 per cent. less than
+the stress in parts connected, and the bearing pressure equal
+to it for single-shear rivets; and 50 per cent. more for rivets
+in double shear, though the two latter values may probably
+approach those for wrought iron in steel of the higher grades
+sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction
+of the nominal working stress, arrived at by any one of the
+methods in use which may be adopted, affecting both the
+parts connected, and the rivets connecting them. For reverse
+stresses it is advisable to keep the shear stress in any
+rivet so low, say 3 tons per square inch, that the frictional
+resistance of the parts gripped by the rivets shall be sufficient
+to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure
+that, if brought to a bearing in one direction by the greater
+force, it shall not go back with reversal of stress. This requirement
+may be open to some question with respect to
+good machine-riveted work, but for hand-riveted connections
+it may certainly be adopted with wisdom.</p>
+
+<p>The following table will show at a glance how the stresses
+proposed vary with the unit stresses governing the main
+sections.</p>
+
+<p class="center"><span class="smcap">Proposed Table of Rivet Stresses.</span></p>
+
+<table class="nowrap" summary="Table page 58">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">Unit<br />Stress<br />in<br />Member.</th>
+<th class="center padl1 padr1 br">Shear<br />Stress.</th>
+<th class="center padl1 padr1 br">Bearing<br />Pressure<br />for<br />Single-Shear<br />Rivets.</th>
+<th class="center padl1 padr1">Bearing<br />Pressure<br />for<br />Double-Shear<br />Rivets.</th>
+</tr>
+
+<tr>
+<td colspan="4" class="center padl1 padr1 highline"><i>Wrought Iron.&mdash;Tons per Square Inch.</i></td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">3&middot;0</td>
+<td class="right padl1 padr2 br">2&middot;7</td>
+<td class="right padl1 padr4 br">3&middot;6</td>
+<td class="right padl1 padr4">5&middot;4</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr2 br">3&middot;6</td>
+<td class="right padl1 padr4 br">4&middot;8</td>
+<td class="right padl1 padr4">7&middot;2</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">5&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;5</td>
+<td class="right padl1 padr4 br">6&middot;0</td>
+<td class="right padl1 padr4">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">6&middot;0</td>
+<td class="right padl1 padr2 br">5&middot;4</td>
+<td class="right padl1 padr4 br">7&middot;2</td>
+<td class="right padl1 padr4">10&middot;8</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td class="right padl1 padr2 br">6&middot;3</td>
+<td class="right padl1 padr4 br">8&middot;4</td>
+<td class="right padl1 padr4">12&middot;6</td>
+</tr>
+
+<tr>
+<td colspan="4" class="center padl1 padr1 highline"><i>Steel.&mdash;Tons per Square Inch.</i></td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr2 br">3&middot;2</td>
+<td class="right padl1 padr4 br">4&middot;0</td>
+<td class="right padl1 padr4">6&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">5&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;0</td>
+<td class="right padl1 padr4 br">5&middot;0</td>
+<td class="right padl1 padr4">7&middot;5</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">6&middot;0</td>
+<td class="right padl1 padr2 br">4&middot;8</td>
+<td class="right padl1 padr4 br">6&middot;0</td>
+<td class="right padl1 padr4">9&middot;0</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">7&middot;0</td>
+<td class="right padl1 padr2 br">5&middot;6</td>
+<td class="right padl1 padr4 br">7&middot;0</td>
+<td class="right padl1 padr4">10&middot;5</td>
+</tr>
+
+<tr>
+<td class="right padl1 padr2 br">8&middot;0</td>
+<td class="right padl1 padr2 br">6&middot;4</td>
+<td class="right padl1 padr4 br">8&middot;0</td>
+<td class="right padl1 padr4">12&middot;0</td>
+</tr>
+
+<tr class="bb">
+<td class="right padl1 padr2 br">9&middot;0</td>
+<td class="right padl1 padr2 br">7&middot;2</td>
+<td class="right padl1 padr4 br">9&middot;0</td>
+<td class="right padl1 padr4">13&middot;5</td>
+</tr>
+
+</table>
+
+<blockquote>
+
+<p><span class="smcap">Note.</span>&mdash;Tension on rivets to be limited to one-half the permissible
+shear stress, the holes being slightly countersunk under snap-head.</p></blockquote>
+
+<p>It may be objected that the shear stresses in the proposed
+table are somewhat high for wrought iron and steel.
+This feature is intentional, and is supported by the consideration<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span>
+that whereas there may be loss of strength in the members
+of a structure by waste, there is no such loss in rivets,
+if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective
+field rivets is left to be dealt with as may be considered
+advisable for each particular case, the table as it stands being
+applicable only to riveting not below the standard of first-rate
+hand work.</p>
+
+<p>Cases of loose rivets in main girders over 50 feet span,
+due to any cause but bad work, are extremely rare, unless
+resulting from the action of some other part of the structure.
+It may be stated broadly that for railway bridges of less than
+perfect design, the nearer the rail, the more loose rivets,
+generally at connections. This is, no doubt, largely due to
+the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span>
+load, and because this effect has been but little modified by
+the elasticity of any considerable length of intervening girder-work.
+In addition to this, it is quite usual to find the rivets
+more heavily stressed, even though the load be considered
+as &#8220;static,&#8221; in the floor system than in the main-girders,
+though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting&mdash;viz., the
+connections&mdash;are commonly dealt with by hand; and for
+this reason it is the more necessary to design these with the
+greatest care.</p>
+
+<p>Any arrangement which favours the gradual acceptance
+of stress by one part from another will contribute to the
+integrity of riveted connections, and lessen the liability of
+the material to develop faults. In other branches of design
+this is well recognised, but appears in much old bridge work
+to have been entirely overlooked.</p>
+
+<p>Bridges carrying public roads very seldom furnish examples
+of loose rivets; the conditions are generally much
+more favourable, impact being practically absent, full loading
+infrequent, and the proportion of dead load to live, high.</p>
+
+<p>It is, perhaps, hardly necessary to insist upon rivets
+being, apart from mere considerations of strength, sufficiently
+near together to insure close work and exclude moisture.
+Outside edge seams should never be more widely spaced
+than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections,
+the greater stiffness of the section makes wider spacing
+allowable up to, say, 20 times the thickness; but this must
+be governed largely by the amount of riveting required to
+pull the parts close together. Where more than four thicknesses
+are to be gripped by the rivets, <sup>3</sup>&#8260;<sub>4</sub> inch in diameter is
+hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed <sup>5</sup>&#8260;<sub>8</sub> inch thick.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span></p>
+
+<h2>CHAPTER VI.<br />
+<span class="chaptitle">HIGH STRESS.</span></h2>
+
+<p>High stress, provided it be well below that at which immediate
+injury results, or possible failure, is not uniformly objectionable.
+It may be first considered relative to the absolute
+and elastic limits of strength, next with respect to the range
+of stress, and, finally, with regard to the frequency of application.
+For practical purposes&mdash;that is, for the continued
+efficiency of a structure&mdash;the limit of elasticity must be considered
+to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long
+as it lasts, be liable to the original measure of stress. There
+may be places in a bridge, however, over-stressed only in the
+earlier period of its existence, which, by being over-stressed
+and suffering deformation, permit the origin of this distortion
+to be harmlessly met in some other way. In such a
+case the injury done to that part does not, of necessity, lead
+to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail
+after being in use but a short time. As for riveting, so in
+dealing with the amount of stress to which a member is
+supposed to be liable, it should be clearly understood by what
+method this has been arrived at, whether the value assigned
+is the actual measure of the stress, or simply the conventional
+amount arrived at in the conventional way; perhaps neglecting
+web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal
+amount of stress, or including only a partial recognition of<span class="pagenum"><a name="Page_62" id="Page_62">[62]</a></span>
+those influences. In any case quoted the stress named is
+that at which the author arrives by the ordinary methods of
+computation carefully applied, where these appear to be
+sufficiently precise, unless any qualifying remark be added.
+Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that
+basis, and deducing the stress at the holes from the ratio of
+net to gross section at the extreme fibres; a method more
+correct than by reference to the moment of inertia of the net
+section. Any exhaustive refinement in the study of stresses
+is not attempted, both because it is beyond the author&#8217;s
+powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation
+in practice. Effective spans are taken at moderate
+values, and all exaggeration is avoided.</p>
+
+<p>The effects of impact in any part vary so much with
+nearness to, or remoteness from, the living load, and the
+frequency of development of the maximum stress from all
+causes acting together is so much affected by the same consideration,
+that it is apparent a nominal stress which may be
+harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as
+ordinarily stated&mdash;i.e., at so much per square inch, uniform
+across a section&mdash;is seldom a cause of trouble. In nearly all
+cases of failure there is an accompanying localised destructive
+stress, either in rivets or elsewhere, with crippling or deformation
+of some essential part. In the tension flanges of main
+girders with uncomplicated stress, this may run up to an
+amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the
+compression flanges, if these be in themselves sufficiently
+stiff, or properly restrained from side flexure. In support of
+the above statement may be quoted the following instances
+relating to wrought-iron structures<span class="nowrap">:&mdash;</span></p>
+
+<p><span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span></p>
+
+<p>A bridge of 60 feet effective span, having girders
+immediately under the rails, had a flange stress of 6&middot;3 tons
+per square inch. Another of 64 feet span, carrying two lines
+of way, with outside main girders and cross-girders, had the
+flanges of the former stressed to 6&middot;8 tons per square inch.
+A third, of 76 feet span, of similar construction to the last,
+was stressed in the main girder flanges to 7&middot;5 tons per square
+inch. The webs were not included in the computation; the
+figures, therefore, compare with ordinary practice. In these
+three cases the main girders showed no signs of distress,
+referable to the results stated, though the top flanges in the
+last case were curved inwards. The effect of this flexing of
+the flange would be, of course, to increase the amount of
+compressive stress along one edge, though to what degree
+cannot now be stated.</p>
+
+<div class="figc600"><a name="Fig43" id="Fig43"></a><a name="Fig45" id="Fig45"></a><a name="Fig44" id="Fig44"></a>
+<p class="caption"><span class="smcap">Fig.</span> 43.</p>
+<img src="images/illo076.png" alt="" width="600" height="308" />
+<p class="caption_b"><span class="left70"><span class="smcap">Fig.</span> 44.</span> <span class="right29"><span class="smcap">Fig.</span> 45.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 44. and <span class="smcap">Fig.</span> 45.</p>
+</div>
+
+<p>A further instance of considerable flange stress occurred
+in a bridge of seven nearly equal continuous spans, 25 feet
+generally, the end and greatest span being 29 feet 6 inches,
+centre to centre of bearings. Some details of the bridge are
+given in <a href="#Fig43">Figs. 43 to 45</a>. The four inner main girders
+under rails were 2 feet deep, with webs <sup>1</sup>&#8260;<sub>2</sub> inch thick over
+piers, and <sup>3</sup>&#8260;<sub>8</sub> inch at abutments, having flanges of two <span class="lettsymb">L</span> bars,
+3 inches by 3 inches by <sup>5</sup>&#8260;<sub>8</sub> inch. There were also two
+outer girders of the same depth, with single <span class="lettsymb">L</span> bars. Plate
+diaphragms of full girder depth and particularly stiff were
+carried right across the bridge at the centre of the spans,
+and over the piers. The girders, though evidently designed
+to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see <a href="#Fig45">Fig. 45</a>).
+It is doubtful if the girders acted with strict continuity for
+long after erection, as the excessive stress in the rivets of the
+flange joint would, for that condition, have been nearly
+sufficient to shear them. It is probable that this being so,
+the joints first yielded, relieving the bending moment over<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span>
+the piers, and increasing it near mid-span. Whether the end
+spans be considered as strictly continuous with the rest, or
+as simple beams, the maximum bending moments would not<span class="pagenum"><a name="Page_65" id="Page_65">[65]</a></span>
+greatly differ, though occurring for continuity over the pier,
+for free beams at the centre. There is, however, an intermediate
+condition which makes the moments at these two
+places less than either maximum, but equal to each other;
+a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been
+calculated, giving the minimum stress value that can be
+accepted. The diaphragm has been assumed to transfer to
+the outer girders a due proportion of the load. With this
+explanation it may now be stated that, under engine loads
+corresponding to those running, the flange stress worked out
+at 7&middot;4 tons per square inch tension, web included, or 9&middot;7
+tons per square inch without considering the web; which
+stresses, it is more than probable, may have been greater.
+The figures include the consideration of anything which may
+contribute to lowering the stress, and are hardly to be compared
+with those worked to in ordinary design of new work,
+in which it would be quite usual to neglect the assistance of
+the outer girders and the webs, to work to heaviest engine-loads,
+and possibly include an allowance for the effects of
+settlement. Dealt with in this way the girders would seem
+to be of about one-fourth the strength that would be required
+in the design of a new bridge, in which certain elements of
+strength would be deliberately ignored.</p>
+
+<p>The ironwork was in good condition, there was no ordinary
+evidence of weakness apart from the calculated results,
+the vibration was distinctly moderate, and the deflection,
+though not recorded, was certainly small. The bridge did,
+indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long
+overstressed may have a sensibly higher modulus of elasticity
+than newer work at more moderate stresses. The traffic was
+not very considerable, and both roads, of the same spans,
+but seldom loaded at the same time; though with this construction<span class="pagenum"><a name="Page_66" id="Page_66">[66]</a></span>
+of bridge there would in either case be very little
+difference. The author recalls no reason for supposing that
+the piers had yielded in any sensible degree. The bridge
+was rebuilt after some thirty-six years&#8217; use.</p>
+
+<p>Stress of considerable amount in the flanges of a latticed
+main girder of 63 feet span has already been noticed in the
+chapter on &#8220;<a href="#Page_45">Riveted Connections</a>,&#8221; which for the tension
+boom worked out to 7&middot;1 tons per square inch, the flanges
+in this case showing no signs of weakness. An instance has
+also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons
+per square inch, the girder recovering its form when relieved
+of load.</p>
+
+<p>As to stress in cross-girder flanges, an example may be
+quoted of a bridge of 109 feet span, carrying two roads,
+having outside main girders, with cross-girders between;
+these latter were stressed in the flanges to 6&middot;7 tons per
+square inch (webs not included), if the partial distribution
+among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some
+reason to think in this instance that distribution had the
+effect of reducing the stress quoted, as the observed deflection
+of the cross-girders was materially less than that calculated
+for girders acting independently of each other, though
+this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the
+heavy main girders, would also tend to moderate the stress.
+No very definite conclusion can therefore be deduced from
+this instance.</p>
+
+<p>To take another case of less uncertainty, the bridge of
+35 feet span (see <a href="#Fig33">Fig. 33</a>), referred to in &#8220;<a href="#Page_45">Riveted Connections</a>,&#8221;
+may again be cited. The extreme fibre stress in the
+cross-girder flanges worked out at 6&middot;3 tons per square inch,
+web included, or 6&middot;5 tons, exclusive of the web. It cannot<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span>
+be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was <sup>1</sup>&#8260;<sub>2</sub> inch on the
+span of 11 feet, in addition to a permanent set of <sup>3</sup>&#8260;<sub>4</sub> inch,
+largely due, however, to &#8220;working&#8221; rivets.</p>
+
+<p>A better and altogether conclusive case of the way in
+which cross-girders may occasionally suffer considerable
+stress, and show no sign, is furnished by two cross-girders,
+of which some particulars are here given. These girders
+occurred in the floor of a very acute angled skew bridge,
+riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end
+on a masonry abutment. The first girder was about 19 feet
+effective span, 12 inches deep in the web, with angle bar and
+plate flanges. The girders were spaced 6 feet apart, and
+were connected under the rails by <span class="lettsymb">T</span>-bars, cranked down to
+face the webs, and riveted through. Though these <span class="lettsymb">T</span>&#8217;s had
+little stiffness, yet the frequent vertical movements of the
+girders relative to each other, under passing loads, had broken
+the majority of the <span class="lettsymb">T</span>-bars at the bends, so that no notice
+need be taken of these as transferring load from any one
+cross-girder to its neighbour. The floor covering consisted
+of timbers about 4 inches thick, also incompetent to transfer
+any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers,
+chairs, and ordinary bull-headed rails. The stress to which
+the girder was liable works out at 8&middot;4 tons per square inch,
+on the extreme fibres of the net section, web included; or
+9&middot;1 tons, neglecting the web, under engine-loads of a
+common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with
+angle bar and plate flanges. The stress per square inch was
+10&middot;5 tons, web included, or 11&middot;1 tons per square inch,
+neglecting the web. This girder carried three rails, one of
+which was near to the abutment bearing, so that there was<span class="pagenum"><a name="Page_68" id="Page_68">[68]</a></span>
+no great difference in the stress induced whether all three rails
+were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a
+common occurrence for the girders to take the full loads.
+The heavier engines passed scores of times in a day&mdash;lighter
+engines probably one hundred times. The bridge was about
+twenty years old, yet these cross-girders, when removed,
+showed no other sign of age and wear than that due to rust.</p>
+
+<div class="figcenter"><a name="Fig46" id="Fig46"></a>
+<img src="images/illo080.png" alt="" width="500" height="241" />
+<p class="caption"><span class="smcap">Fig.</span> 46.</p>
+</div>
+
+<p>All the foregoing instances relate to wrought-iron bridges.
+Two cases of steel construction are here added, the first of
+these furnishing an example of high girder stress somewhat
+remarkable. This was found in a trough girder of a strange
+pattern, of which a section is here given (<a href="#Fig46">Fig. 46</a>). The
+bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a
+crawling pace. The larger of the two girders carrying the
+rails was 15 feet 8 inches effective span. The sides of the
+trough consisted each of two vertical plates, originally <sup>1</sup>&#8260;<sub>2</sub> inch
+thick, but wasted to an aggregate thickness of <sup>5</sup>&#8260;<sub>8</sub> inch.
+These plates 6 inches deep, were connected at their lower
+edges to angle bars, 3 inches by 3 inches by <sup>1</sup>&#8260;<sub>2</sub> inch, which
+again were riveted to a bottom plate 16 inches wide,
+originally <sup>1</sup>&#8260;<sub>2</sub> inch thick, wasted to <sup>3</sup>&#8260;<sub>8</sub> inch. Lying in the bottom<span class="pagenum"><a name="Page_69" id="Page_69">[69]</a></span>
+of the trough, and riveted through the inner angle flanges,
+was a bridge-rail. Assuming that the metal retained its
+elastic properties from top to bottom of the section, at
+whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the
+net section. As puddled steel, of which the girders were
+made, may have a tenacity of 45 to 55 tons per square inch,
+the assumption is probably correct. The author has no
+record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine
+passing over, required some determination.</p>
+
+<p>A point of additional interest in this little bridge is that,
+though made of steel, it dates as far back as 1861, having
+been in use thirty-two years when removed. The particular
+variety of steel used was known as Firth&#8217;s puddled. The
+evidence of this consists in correspondence showing that permission
+had been asked of the controlling authority, by the
+only users of the siding, to apply this material, with no evidence
+of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some
+girders of considerable span. The appearance of the trough
+girders to which the foregoing particulars apply was distinctly
+different to that which might be expected in ordinary
+wrought iron. The top edges of the vertical plates were
+wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which
+the girders held up to their work for so long is, by itself,
+conclusive on the point. The bridge-rail appeared to be of
+wrought iron, the different modulus of elasticity of which
+has been included in the calculation upon which the preceding
+results are based. That these girders stood so well is,
+perhaps, largely due to the fact that the load carried by them
+was, though varying within wide limits, practically free from
+impact, which, had the load passed over quickly, would, with<span class="pagenum"><a name="Page_70" id="Page_70">[70]</a></span>
+girders so small, shallow and flexible, have been very sensible.</p>
+
+<p>The second instance of steel construction in which somewhat
+high stress is manifest is that of some steel troughing of
+the Lindsay pattern, used in a bridge built in 1885. The
+troughs ran parallel to the rails, having an effective span of
+18 feet 8 inches. The depth of the section (which is shown
+in <a href="#Fig47">Fig. 47</a>), was 8<sup>1</sup>&#8260;<sub>2</sub> inches, making a ratio of depth to span
+of <sup>1</sup>&#8260;<sub>28</sub>. The road was of ballast, sleepers, chairs, and 85-lb.
+rails.</p>
+
+<div class="figcenter"><a name="Fig47" id="Fig47"></a>
+<img src="images/illo082.png" alt="" width="400" height="208" />
+<p class="caption"><span class="smcap">Fig.</span> 47.</p>
+</div>
+
+<p>Assuming this to be carried on six troughs, which corresponds
+to 11 feet 3 inches of width, the extreme fibre stress
+works out at 7&middot;5 tons per square inch, under usual engine-loads.
+The bridge when examined after fourteen years&#8217; use was
+in good condition, and at that time but little rusted; but the
+end seam rivets were, as is not uncommon with such troughing,
+loose. The traffic over the bridge was considerable, but
+not at great speed.</p>
+
+<p>On the opposite page are set out the results which have
+been given, in tabulated form, as was done for rivet stresses,
+to enable ready comparison to be made.</p>
+
+<p class="center"><span class="smcap">Examples of High Stress.</span><span class="pagenum"><a name="Page_71" id="Page_71">[71]</a></span></p>
+
+<table class="nowrap" summary="Table page 71">
+
+<tr class="bt bb">
+<th rowspan="2" colspan="3" class="center padl1 padr1 br">&mdash;</th>
+<th rowspan="2" colspan="4" class="center padl1 padr1 br">Span<br />in<br />Feet.</th>
+<th rowspan="2" class="center padl1 padr1 br">Part<br />Stressed.</th>
+<th colspan="2" class="center padl1 padr1 br">Stress per<br />Square Inch.</th>
+<th rowspan="2" class="center padl1 padr1 br">Tension<br />or<br />Compression.</th>
+<th rowspan="2" colspan="4" class="center padl1 padr1">Condition.</th>
+</tr>
+
+<tr class="bb">
+<th class="center padl1 padr1 br">Webs<br />Included.</th>
+<th class="center padl1 padr1 br">Webs not<br />Included.</th>
+</tr>
+
+<tr>
+<td class="center padl1 wrappable">Wrought-iron</td>
+<td class="center wrappable">main girders,</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">60&middot;0</td>
+<td rowspan="3" colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">Flange</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td rowspan="3" colspan="3">&nbsp;</td>
+<td class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">64&middot;0</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;8</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">76&middot;0</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">7&middot;5</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td rowspan="2" class="center">&#8222;</td>
+<td rowspan="2" class="center">&#8222;</td>
+<td rowspan="2" class="center br">&#8222;</td>
+<td rowspan="2" class="right padl1 padr1">29&middot;5</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="2" class="br narrow">&nbsp;</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr3 br">7&middot;4</td>
+<td class="right padl1 padr3 br">9&middot;7</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1">Good.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="right padl1 padr3 br">8&middot;3</td>
+<td class="center padl1 padr1 br">Compression</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="left padl1 padr1 br">lattice</td>
+<td class="right padl1 padr1">63&middot;0</td>
+<td rowspan="6" colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">&#8222;</td>
+<td colspan="2" class="center padl1 padr1 br">7&middot;1</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td rowspan="6" colspan="3">&nbsp;</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">47&middot;0</td>
+<td class="center padl1 padr1 br wrappable">Flange edge</td>
+<td class="right padl1 padr3 br">10&middot;0</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">Compression</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center padl1 wrappable">Wrought-iron</td>
+<td class="center wrappable">cross-girders,</td>
+<td class="left padl1 padr1 br">plate</td>
+<td class="right padl1 padr1">26&middot;0</td>
+<td class="center padl1 padr1 br">Flange</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="right padl1 padr3 br">6&middot;7</td>
+<td class="center padl1 padr1 br">Tension</td>
+<td class="left padr1">Fair.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">11.0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">6&middot;3</td>
+<td class="right padl1 padr3 br">6&middot;5</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Bad; loose rivets.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">19&middot;0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">8&middot;4</td>
+<td class="right padl1 padr3 br">9&middot;1</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Good, but rusted.</td>
+</tr>
+
+<tr>
+<td class="center">&#8222;</td>
+<td class="center">&#8222;</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr1">22&middot;0</td>
+<td class="center br">&#8222;</td>
+<td class="right padl1 padr3 br">10&middot;5</td>
+<td class="right padl1 padr3 br">11&middot;1</td>
+<td class="center br">&#8222;</td>
+<td class="left padr1 wrappable">Good, but rusted.</td>
+</tr>
+
+<tr>
+<td rowspan="2" colspan="3" class="left padl1 padr1 br">Steel trough girder</td>
+<td rowspan="2" class="right padl1 padr1">15.7</td>
+<td rowspan="2" class="right padr0 narrow">-</td>
+<td rowspan="2" class="bt bb bl narrow">&nbsp;</td>
+<td rowspan="2" class="br narrow">&nbsp;</td>
+<td class="center br">&#8222;</td>
+<td colspan="2" class="center br">15&middot;0</td>
+<td class="center br">&#8222;</td>
+<td rowspan="2" class="narrow">&nbsp;</td>
+<td rowspan="2" class="bt br bb narrow">&nbsp;</td>
+<td rowspan="2" class="left padl0 narrow">-</td>
+<td rowspan="2" class="left padr1 wrappable">Fair, but rusted.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br wrappable">Top edge</td>
+<td colspan="2" class="center br">32&middot;0</td>
+<td class="center br">Compression</td>
+</tr>
+
+<tr class="bb">
+<td colspan="3" class="left padl1 padr1 br">Steel troughing</td>
+<td class="right padl1 padr1">18&middot;7</td>
+<td colspan="3" class="br">&nbsp;</td>
+<td class="center padl1 padr1 br">Flanges</td>
+<td class="right padl1 padr3 br">7&middot;5</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br wrappable">Tension and Compression</td>
+<td colspan="3">&nbsp;</td>
+<td class="left padr1">Fair, but rusted.</td>
+</tr>
+
+</table>
+
+<p>It would be unwise to infer from the instances which<span class="pagenum"><a name="Page_72" id="Page_72">[72]</a></span>
+have been quoted that high stress may be regarded with
+complaisance. In the most conscientious engineering work
+there should still be a liberal margin for material possibly
+defective, or even bad, for waste and deterioration, and for
+the aggregate effect of minor errors in design, any one of
+which considerations, except the first, by itself might not be
+of great importance. The conclusion which may, however,
+be derived from this and the previous chapters is, that bridge
+failures are less likely to occur from high stress of a kind
+readily calculated than from failure in detail, obscure and
+little suspected, the reason for which is not perhaps apparent,
+till the attention is forcibly directed to it by the refusal of
+the structure to sustain the forces to which it may be liable.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_73" id="Page_73">[73]</a></span></p>
+
+<h2>CHAPTER VII.<br />
+<span class="chaptitle">DEFORMATIONS.</span></h2>
+
+<p>Instructive lessons are to be had from a study of the
+various alterations in form to which metallic bridgework is
+liable, which alterations may be due simply to the development
+of stress of ordinary amount, and are then generally
+small; or to abnormal stresses, the result of some distortion
+in the bridge structure itself not originally intended, and
+possibly extreme. In addition to these there may be deformations
+due to settlement, to &#8220;creeping&#8221; of parts of the
+structure relative to the rest, to temperature changes, to rust,
+and to original bad workmanship. In any instance quoted
+below the methods adopted to ascertain the amounts of such
+alterations were quite simple, even crude; but as care was
+exercised, and no attempt made to measure any very minute
+changes, the results may be accepted as practically correct.</p>
+
+<p>Dismissing for the present changes of form such as are
+to be expected, and touched upon in other places in this
+work, with respect to the particular parts of bridge structures
+affected by them, a few instances will be adduced of
+alterations which, though not very surprising, are such as in
+the design of the work are hardly likely, in most instances,
+to have been contemplated.</p>
+
+<p>A case has already been referred to in which, owing to
+eccentric loading of main girders, these were, as to the top
+flanges, flexed sideways a considerable amount. It is proposed
+to supplement this by further remarks relative to
+somewhat similar cases. A like effect is frequently to be<span class="pagenum"><a name="Page_74" id="Page_74">[74]</a></span>
+observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting
+ledges formed by the bottom angle-bars of such troughs.
+In old forms of this arrangement it is common to find the
+two girders forming the trough connected only by bolts
+passing through the timbers, or just above them and below
+the rails; or connected by narrow strips, which serve no
+other purpose than to prevent the sides spreading at the
+bottom. The top flanges in such cases commonly curve
+inwards on the passage of the running load, accompanied of
+necessity by an increase of compressive stress upon the outer
+edges of the flanges, and perhaps by the working of any
+flange-joint which may exist. This, both as to flexing of
+the top flange and the working of a joint, was noticed in
+the case of a bridge twenty-three years old, very similar to
+that illustrated in <a href="#Fig8">Figs. 8</a> and <a href="#Fig9">9</a>, and described on <a href="#Page_13">pages 13</a>
+and <a href="#Page_14">14</a>. The top flange consisted, however, of a bridge rail
+riveted to the top edge of the web, butting at a joint, and
+covered by thick cover strips (see <a href="#Fig48">Fig. 48</a>). The joint itself
+was poor, and depended largely upon the character of the
+butt, which was not sufficiently good to prevent the top
+member kinking at this point, under the joint influence of
+transverse effort and compressive stress, with possibly some
+help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked
+in passing that it is very objectionable to use bolts as was
+done in this instance; for as the timber settles down on its
+seat, taking the bolts with it, these bear hard in the webs,
+enlarging or even, as in this case, tearing the holes, accompanied
+by injury to the bolts themselves. The practice is
+now almost obsolete, but the example is instructive as showing
+the impropriety of securing timbers by bolts passing through
+them at right angles to the action of the load, unless these
+bolts are quite free to move with the timber as it compresses.</p>
+
+<p><span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span></p>
+
+<p>If trough girders must be used, the better plan is to
+connect the two sides by a continuous bottom plate, the
+trough thus formed being properly drained, if the timber
+is not bedded in asphalt concrete; or to introduce stiff
+diaphragms at intervals beneath timbers, if the depth
+suffices.</p>
+
+<p>In the case just quoted the curvature of the top members
+of the girders was inwards, but in the instance given below,
+of twin girders 26 feet effective span, with longitudinal
+timbers between, resting, as before, upon the inner ledge
+formed by the bottom flanges, the curvature was observed in
+three out of four girders to be <sup>1</sup>&#8260;<sub>2</sub> inch in a contrary direction,
+the fourth remaining straight.</p>
+
+<div class="figc450"><a name="Fig48" id="Fig48"></a><a name="Fig49" id="Fig49"></a>
+<img src="images/illo087.png" alt="" width="450" height="201" />
+<p class="caption_b"><span class="left35"><span class="smcap">Fig.</span> 48.</span> <span class="right64"><span class="smcap">Fig.</span> 49.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 48. and <span class="smcap">Fig.</span> 49.</p>
+</div>
+
+<p>An inspection of the accompanying section, <a href="#Fig49">Fig. 49</a>, will,
+perhaps, render the reason evident when it is noticed that
+the top members are very unsymmetrical in form, the effect
+of this being to give these members, under stress, a strong
+tendency to flex outwards, apparently more than sufficient
+to counteract the tendency of an eccentric application of
+load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be
+not materially in excess, and is actually so, only because the
+thinness of the web&mdash;<sup>1</sup>&#8260;<sub>4</sub> inch&mdash;renders it incompetent to keep
+the bottom flange up to its work, and so secure the full
+effect of the eccentric loading in limiting the outward tendency,<span class="pagenum"><a name="Page_76" id="Page_76">[76]</a></span>
+due to the section of the top member, the effects of
+which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange
+to the other prevent the want of symmetry noticed in these&mdash;which,
+by the way, is on the wrong side for utility&mdash;from
+having any particular effect.</p>
+
+<p>To give one other example of the consequences of eccentric
+loading, a bridge of 48 feet effective span may be quoted.
+This bridge carried four lines of way supported by five main
+girders, trussed by kicking-struts in such a manner as to form
+a bastard arch. A part section and plan are given in <a href="#Fig50">Figs.
+50</a> and <a href="#Fig51">51</a>.</p>
+
+<div class="figcenter"><a name="Fig50" id="Fig50"></a>
+<img src="images/illo089a.png" alt="" width="450" height="482" />
+<p class="caption"><span class="smcap">Fig.</span> 50.</p>
+</div>
+
+<div class="figcenter"><a name="Fig51" id="Fig51"></a>
+<img src="images/illo089b.png" alt="" width="500" height="198" />
+<p class="caption"><span class="smcap">Fig.</span> 51.</p>
+</div>
+
+<p>The floor consisted of Lindsay&#8217;s troughing resting upon
+the lower flanges of the main girders, the three middle
+girders, subject to eccentric loading, sometimes on one side,
+sometimes on the other, were, with dead load only, straight;
+but the two outer girders, liable to loading only on one side,
+had, under repeated applications of such a load, assumed a
+permanent curve towards the rails&mdash;<sup>13</sup>&#8260;<sub>16</sub> inch in one case and
+1 inch in the other&mdash;which curvature, no doubt, increased
+when a live load came upon the contiguous roads, though
+this was not measured. It should be remarked in passing
+that, owing to settlement and the canting of the abutments,
+the three middle girders were also &#8220;down&#8221;&mdash;in one case <sup>3</sup>&#8260;<sub>4</sub>
+inch. The girders, with one near road loaded, deflected <sup>1</sup>&#8260;<sub>8</sub> inch&mdash;greatly
+less than would have been the case had the main
+girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.</p>
+
+<p>Deformations due to settlement may be very considerable.
+The author recalls two instances affecting continuous girders.
+In the first of these, a bridge twenty years old, of two spans
+of about 50 feet each, and with girders 4 feet 6 inches deep,
+the centre pier had sunk 4 inches, reducing the spans, as
+respects the dead load, practically to the condition of simple<span class="pagenum"><a name="Page_77" id="Page_77">[77]</a><br /><a name="Page_78" id="Page_78">[78]</a></span>
+beams, just resting, but hardly bearing, upon the piers when
+free of live load.</p>
+
+<p>In the second case, also of two openings of about 55 feet
+each, with girders 8 feet deep, one abutment had sunk about
+3 inches, more than doubling the stresses over the centre
+pier. It is manifest that continuous girders should only be
+adopted where settlement of the supporting points is not
+likely to occur to any material degree. If this cannot be
+relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to
+make a liberal allowance for settlement stresses, in which
+case any economical advantage that should exist will probably
+disappear. It is, however, to be acknowledged that so long
+as the girders are in touch, under dead load, with the bearings
+intended to support them, the stresses due to a live load
+are unaltered, the principal effect in this case being that the
+variation in stress due to the live load ranges between limits
+that are higher or lower in the scale of stress than is the
+case with bearings undisturbed; still, if it is desired that
+the maximum stress shall not exceed, say, 6 tons per square
+inch, it can hardly be a matter of indifference that settlement
+shall induce a maximum of, perhaps, 10 tons, as in that case
+the stress must be 4 tons nearer the limit of statical strength.</p>
+
+<p>Before leaving this matter it may be well to point out
+that in the case of continuous girders of uniform section a
+moderate settlement of the piers may even be advantageous
+by reducing the moments over the piers, and possibly making
+them equal to those obtaining near the middle of the spans,
+in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.</p>
+
+<p>Bridges consisting of simple main girders connected by
+cross-girders may be very prejudicially affected by unequal
+settlement; for instance, if one girder bearing settles more
+than the others, a twist is put upon the structure very trying<span class="pagenum"><a name="Page_79" id="Page_79">[79]</a></span>
+to the floor-girder connections, and possibly to the main
+girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments.
+Indeed, settlement of this kind may be much more destructive
+to a metallic bridge than to an arch of brick or masonry,
+the commonly accepted opinion notwithstanding.</p>
+
+<p>Instances of deformations due to the creeping of some
+part of the structure away from its work, are within the
+author&#8217;s knowledge, rare; except in the case of the ends of
+main girders in skew bridges, already referred to.</p>
+
+<p>Distortion, the result of temperature changes, is frequently
+to be observed in any considerable length of girder
+flange or parapet where there is not freedom of movement,
+unless due provision is made to check it.</p>
+
+<p>It is quite common to see parapets out of line, either
+because the ends are not free, or because the light work of
+the parapet being more exposed to the sun&#8217;s rays than the
+girder work to which the lower part is attached, expanding
+to a greater degree, is subject to considerable compressive
+force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or
+flexible joints at moderate distances apart, or to make the
+parapet sufficiently stiff to take the stresses developed, without
+crippling. A parapet may also go out of shape if directly
+attached to the top flange of a girder liable to heavy loading,
+particularly if the girder be shallower than the parapet,
+simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the
+girder proper.</p>
+
+<p>Rivets spaced too far apart, by allowing the plates or
+other parts to spring open slightly, and permitting moisture
+to enter, results in the growth of rust, which, as it swells in
+forming, forces the parts asunder, and may set up considerable
+stress.</p>
+
+<p><span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span></p>
+
+<p>Flat bars riveted together by rivets spaced 12 inches
+apart may from this cause be forced asunder, as much as <sup>1</sup>&#8260;<sub>2</sub>
+inch, sufficient to set up a stress, with any practicable thickness
+of bar, much exceeding the elastic limit.</p>
+
+<p>Local distortions may occur as the result of imperfect
+workmanship or careless erection, causing quite possibly very
+severe local stresses; or girder flanges may be out of straight
+as a result of riveting up along one side first, instead of
+advancing the riveting simultaneously along the whole
+breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is
+sometimes done to girderwork during manufacture by rough
+treatment to make the work come together; but the author
+has little to offer with respect to these matters that is not
+common knowledge. It may, however, be pointed out in
+passing that a bridge upon the design of which great care
+has been expended, with the idea that theoretical propriety
+shall not be violated, may be completely spoiled in this
+respect by careless construction. Fortunately, both steel
+and wrought iron, if of good quality, are long suffering.
+Incompetent erection will sometimes result in the true girder
+camber not appearing, or in differences as between girders
+supposed to be similar. This is not, of course, a deformation
+in the sense in which the word has previously been used, but
+it is desirable to bear the fact in mind as a possible cause of
+defective camber in dealing with questions of deformation.</p>
+
+<p>The foregoing has reference chiefly to alterations of form
+in bridgework of wrought iron or steel, but a case of considerable
+interest is that of a cast-iron arched structure, of
+which the author made a very complete examination.</p>
+
+<div class="figcenter"><a name="Fig52" id="Fig52"></a>
+<img src="images/illo093a.png" alt="" width="600" height="119" />
+<p class="caption"><span class="smcap">Fig.</span> 52.</p>
+<p class="largeimg"><a href="images/lg093a.png">Large image</a> (41 kB)</p>
+</div>
+
+<div class="figcenter"><a name="Fig53" id="Fig53"></a>
+<img src="images/illo093b.png" alt="" width="600" height="157" />
+<p class="caption"><span class="smcap">Fig.</span> 53.</p>
+</div>
+
+<p>This bridge, built in 1839, and carrying two lines of
+railway, consisted of three spans, 100 feet each, of 10 feet
+rise, made up of four inner and two outer ribs, each rib
+being in three nearly equal parts; the floor was of timber,<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span>
+the abutments and piers of masonry. As originally constructed
+there was no bracing between the ribs other than
+the frames indicated on the plan here given (<a href="#Fig52">Fig. 52</a>),<span class="pagenum"><a name="Page_82" id="Page_82">[82]</a></span>
+stretching from outer rib to outer rib in the neighbourhood
+of the rib joints, which were simple butts without bolts or
+any equivalent means of connection. The floor was, however,
+braced in the horizontal plane, and the structure was
+also braced over the masonry piers. After forty-two years&#8217;
+use supplementary distance-pieces were introduced between
+the ribs, but still no bracing between them, or any efficient
+means of checking lateral movement. A crack developing
+in one of the outer ribs at the crown, led to an investigation
+to trace the cause, the bridge then being fifty-four years old.
+Careful plumbing of the abutments revealed the fact that
+three out of four abutment pilasters were out of the vertical,
+as shown in <a href="#Fig52">Figs. 52</a> and <a href="#Fig53">53</a>, the greatest amount being
+<sup>5</sup>&#8260;<sub>8</sub> inch in 6 feet&mdash;at that corner from which the cracked rib
+had its springing; there was also other evidence of settlement
+in an old crack extending from the top of the abutment
+to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were
+also out of plumb, that which was cracked being 2<sup>1</sup>&#8260;<sub>2</sub> inches
+out at the centre. The joints of the ribs, which, as already
+stated, were simple butts, in some cases opened and shut, as
+the load passed over, in such a way as to suggest that the
+ribs were acting, in a manner, as four-hinged arches, of
+which two hinges were at the springing, and the other two
+at the joints, one of which would for most positions of the
+load be out of use, reducing the rib to the three-hinged condition;
+in other words, as the rolling load passed over the
+span, one or other of the two joints of a rib would &#8220;gape&#8221;
+an appreciable amount at the bottom or at the top. Observations
+were taken by means of a theodolite placed below,
+either upon the bank or upon the tops of the masonry piers,
+sighting upon suitable scales attached to the ribs to ascertain
+the amounts of vertical and horizontal movement during the<span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span>
+passage of trains over the bridge. The principal results are
+set forth in the following table<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Movements of Cast-Iron Ribs under Live Load in a Bridge<br />
+of Three 100-Ft. Spans.</span></p>
+
+<table class="nowrap" summary="Table page 83">
+
+<tr class="bt bb">
+<th colspan="3" class="center padl1 padr1 br">&mdash;</th>
+<th class="center padl1 padr1 br">Fall<br />in<br />Inches.</th>
+<th class="center padl1 padr1 br">Rise<br />in<br />Inches.</th>
+<th class="center padl1 padr1">Lateral<br />Movement<br />in Inches.</th>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 1.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">A.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;20</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1">&middot;04</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">A.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1 br">&middot;03</td>
+<td class="center padl1 padr1">&middot;04</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">B.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;14</td>
+<td class="center padl1 padr1 br">No record.</td>
+<td class="center padl1 padr1">&middot;02</td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 2.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">C.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;40</td>
+<td class="center padl1 padr1 br">&middot;13</td>
+<td class="center padl1 padr1">Slight.</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">C.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;10</td>
+<td class="center padl1 padr1 br">&middot;05</td>
+<td class="center padl1 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Span No. 3.</i></td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1">At</td>
+<td class="center padl1 padr1">D.</td>
+<td class="left padr1 br">Up road loaded</td>
+<td class="center padl1 padr1 br">&middot;22</td>
+<td class="center padl1 padr1 br">No record.</td>
+<td class="center padl1 padr1">No record.</td>
+</tr>
+
+<tr class="bb">
+<td class="center padl1 padr1">&#8222;</td>
+<td class="center padl1 padr1">D.</td>
+<td class="left padr1 br">Down road loaded</td>
+<td class="center padl1 padr1 br">&middot;15</td>
+<td class="center padl1 padr1 br">Slight.</td>
+<td class="center padl1 padr1">Slight.</td>
+</tr>
+
+</table>
+
+<blockquote>
+
+<p><span class="smcap">Note.</span>&mdash;The lateral movements are to either side of the mean
+position.</p></blockquote>
+
+<p>The particulars for spans 2 and 3 were obtained with
+the instrument set up on the pier between these spans. The
+tremor of this pier was such that no useful readings for
+lateral movement could be obtained. Further, as the rolling
+load came upon these spans, the effect was to rock the pier
+to an extent vitiating the readings for vertical displacement;
+but by sighting upon the fixed abutment, and observing the
+amount of this rocking, suitable corrections were made in
+the apparent rib movements. The figures given in the table
+are thus corrected. The pier rocking was equivalent, as an
+extreme, to an inclination from the vertical of 1 in 3200.
+An attempt to measure the horizontal movement of the pier-top<span class="pagenum"><a name="Page_84" id="Page_84">[84]</a></span>
+was unsuccessful, owing to the impracticability of setting
+up the instrument in a suitable position, sufficiently near to
+the pier to enable readings to be satisfactorily taken. This
+horizontal displacement probably amounted to about <sup>1</sup>&#8260;<sub>16</sub> inch
+either way. The rise and fall of the arches, and rocking
+either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect
+to the spans. Summarising the results, the greatest vertical
+movements downwards were 0&middot;20 inch, 0&middot;40 inch, and 0&middot;22
+inch for spans Nos. 1, 2, and 3, the upward movements being
+0&middot;08 inch and 0&middot;13 inch for the first and second spans,
+there being no recorded result of this kind for the third
+span. With adjacent ribs loaded, the movement of the
+ribs unloaded was one from one-third to one-half of the full
+amounts. It is to be noted that the lateral displacement in
+no case exceeded 0&middot;04 inch either way, nor were the vertical
+movements exceptional; yet, as a matter of sensation, when
+seated upon the ironwork, it was a little difficult to believe
+them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0&middot;45
+inch, 0&middot;45 inch, and 0&middot;55 inch for the spans in order, the
+extreme temperatures being fairly representative of the
+English winter and summer. The structure was, as a consequence
+of the examination, efficiently braced by diaphragms
+between the ribs, and diagonals following the arch ribs round
+from springing to springing, with satisfactory results. The
+crack already referred to, and its probable causes, will be
+dealt with under &#8220;<a href="#Page_141">Cast-Iron Bridges</a>.&#8221; Eventually this
+bridge was reconstructed to meet the requirements of growing
+engine-loads.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span></p>
+
+<h2>CHAPTER VIII.<br />
+<span class="chaptitle">DEFLECTIONS.</span></h2>
+
+<p>Deflection, considered only as a fraction of the span, and
+without regard to other conditions affecting it, is of very
+little use as an indication of a girder&#8217;s fitness for its work;
+but when taken with reference to the depth of the girder,
+the nature and amount of the load producing flexure, and,
+further, with regard to the quality of the workmanship and
+normal properties of the material of which the beam is constructed,
+it may be of some little service in helping to form
+a reliable opinion. This consideration applies with less
+force, perhaps, to new work than to old, in which there may
+be unknown influences at work, or unknown defects which
+by excessive deflection may be betrayed. Though too much
+importance should not be attached to results of deflection
+tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each
+case, gives a good general idea of what may be expected in
+a fresh instance, any material departure from which should
+be a reason for specific inquiry as to the cause. A further
+reason with new work is found in the evidence it affords as
+to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case
+of floor beams, in what way the load is distributed amongst
+them, if, indeed, there be any such distribution.</p>
+
+<p>The author has commonly found that new work gives
+greater deflections than old&mdash;i.e., while calculation gives
+the same result for each, it does not apply equally well to
+both. The differences may be accidental, but are probably<span class="pagenum"><a name="Page_86" id="Page_86">[86]</a></span>
+due to other causes, perhaps to the fact that new work has
+not by repeated applications of load lost the resilience of
+parts liable to considerable local stress, such as is very liable
+to occur at connections, so that the deflection is, whilst new,
+greater than after many years&#8217; use, by which time such parts
+may develop a definite &#8220;set,&#8221; and contribute in a less degree,
+or not at all, to the total elastic deformation.</p>
+
+<p>It is also possible, as already suggested, that repeated
+high stress may reduce the ratio of strain to stress, the
+material gradually becoming more rigid, the modulus of
+elasticity being, in fact, increased.</p>
+
+<p>In girders of ordinary construction, the major part of
+the deflection is due to the booms, the remainder to the web;
+the latter is for plate girders a small amount only, and is
+commonly neglected, but for open web constructions it may
+be quite appreciable. For any given type of web arrangement
+the deflection due to the web will, for all depths, remain
+a constant quantity for the same span and unit stress; and
+though a moderate fraction of the whole deflection for a
+shallow girder, it may be a very considerable part for a girder
+of great depth, in which that part due to the booms is, of
+course, smaller, since the deflection due to these varies
+inversely as the girders&#8217; depths.</p>
+
+<p>Deflection, being dependent upon the elasticity of the
+material, is of necessity very largely influenced by the value
+of its modulus E, itself liable to considerable variation, and
+is increased in a small degree by the yield of joints and rivets,
+which effect, apart from the initial &#8220;set&#8221; of the girders,
+appears to be negligible. The stiffness of members in resisting
+angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less,
+and, finally, section excess at joints and gusset attachments
+has an influence in modifying deflection as compared with
+that due to the normal gross sections simply.</p>
+
+<p><span class="pagenum"><a name="Page_87" id="Page_87">[87]</a></span></p>
+
+<p>From these considerations it is apparent that any simple
+deflection formula must be largely empiric in its nature.
+For plate girders of uniform depth and flange stress, the
+writer has found the following to give good results<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D &times; C</span></span> &times; <i>f</i> = deflection in inches.</p>
+
+<p>The span S and depth D are, as a matter of convenience,
+taken in feet; the constant C is for wrought iron 3500, and
+for mild steel 4000; <i>f</i> is the mean of the extreme tensile
+and compressive stresses of the booms, in tons per square
+inch, estimated upon the gross sections.</p>
+
+<p>This, though satisfactory for plate girders, is not so suited
+to girders having open webs, in which the deflection will
+more nearly be</p>
+
+<p class="formula"><span class="fsize150">(</span><span class="division"><span class="num">3S</span><span class="denom">C</span></span> + <span class="division"><span class="num">S<sup>2</sup></span><span class="denom">D &times; C</span></span><span class="fsize150">)</span> &times; <i>f</i>,</p>
+
+<p>the constant C being 3900 and 4450 for iron and steel respectively.
+The latter values of C correspond to normal
+values of the modulus of elasticity of 11,700 and 13,350 tons
+for iron and for steel, it being assumed that any slight rivet
+yield is off-set by any small section excess&mdash;say, 5 per cent.;
+it may, however, happen that section excess is greater than
+assumed, in which case some allowance may properly be made
+for this by increasing C.</p>
+
+<p>To adapt the formul&aelig; to girders other than those having
+parallel booms and uniform stress, the results, as deduced
+above, may be multiplied by constants given in column B of
+the Table given on <a href="#Page_93">page 93</a>.</p>
+
+<p>The practice of adopting for E in deflection formul&aelig; a
+quantity much smaller than its nominal amount, with the
+object of allowing in riveted girder work for the yield of
+rivets and of joints, can hardly now be defended, whatever
+may have been a case at a time when workmanship was much<span class="pagenum"><a name="Page_88" id="Page_88">[88]</a></span>
+inferior, when there was no machine riveting, and joints
+were, owing to the small weight of plates and bars, three
+times as numerous.</p>
+
+<p>The initial &#8220;set&#8221; of a girder consequent upon first loading
+is a quantity quite distinct from deflection proper, and may
+be so small as to be negligible, or read 10 per cent. of the
+true deflection, varying with design and workmanship.</p>
+
+<p>No estimate of girder deflection can be even approximately
+true if there is, at the level of the top or bottom flanges, a
+plated or otherwise rigid floor system which is not taken into
+account, as this will have the effect of very materially reducing
+the boom stress. To neglect this influence, where it
+exists, must necessarily lead to disappointing results, and it
+is quite practicable in many instances to include it in the
+calculation.</p>
+
+<p>The influence of angular distortion between the various
+members has been neglected. It may be pointed out, however,
+that the resistance accompanying these movements in
+girders having riveted connections, though unimportant as
+affecting deflection, is worth some consideration in regard
+to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount
+for any span, but will generally be of less importance in large
+girders than in small, because in large girders the ratio of the
+breadth of members to their length is commonly less.</p>
+
+<p>When determining the probable deflection of any girder
+of exceptional figure, it will be found convenient to make a
+strain diagram&mdash;an old device, in which the actual alterations
+of length being ascertained for all members, the girder is
+carefully set out to a suitable scale, with the lengths of
+members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the
+probable deflection. The value of E for this purpose should
+never be taken at less than the normal amount, and may for<span class="pagenum"><a name="Page_89" id="Page_89">[89]</a></span>
+a considerable excess of metal in joints and gussets be made
+as much as 10 per cent. greater, this being a convenient
+means of making the necessary correction.</p>
+
+<p>The effect of loads quickly applied may here be considered
+in connection with elastic deformations of girders
+of the same span, but different depths. If these be designed
+for similar loads and unit stresses, the deflections due to
+webs and booms of the girders compared will bear the same
+relation, each to each, as do the weights, whether in both
+cases the loads be inert or quickly applied, from which it
+follows that the mechanical &#8220;work&#8221; done by the loads in
+falling through the deflection heights is, neglecting inertia,
+always in proportion to the girderwork weights, and is a
+similar amount per ton, which as the total length of members
+remains substantially unaltered, corresponds to a similar
+amount of work per unit of section, or similar stress, irrespective
+of the depth of the girders.</p>
+
+<p>But for a &#8220;drop&#8221; load, as when there is some obstruction
+upon a railway bridge, there will be in addition a further
+amount of work to be absorbed, which is to be considered
+the same whatever the girder&#8217;s depth, and will for deep
+girders be a larger amount per ton of girderwork than in
+those that are shallow; this, taking effect on members of
+the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in
+the booms.</p>
+
+<p>The influence of the girder&#8217;s inertia in modifying drop-load
+effects will also be less marked in deep&mdash;i.e., light&mdash;girders
+than in girders shallow and heavy.</p>
+
+<p>It is, notwithstanding all this, desirable that the depth
+of main girders should be liberal for economy&#8217;s sake, and
+also that of floor beams, for reasons already dealt with; the
+probability of the drop load is somewhat remote, and, though
+possible, would simply induce, if it occurred, an increment<span class="pagenum"><a name="Page_90" id="Page_90">[90]</a></span>
+of stress rather more important in deep girders, making it
+specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact
+effects.</p>
+
+<p>It should be remarked that for short and very flexible
+beams, generally outside the limits of practice, there may
+also be, under quickly moving loads, a material increase of
+stress due to the centrifugal effort of the load on running
+round the deflection curve, and in rising upon the steep part
+of the curve beyond the girder&#8217;s centre. Where advisable,
+these effects may be modified by cambering the rail.</p>
+
+<p>For pin bridges in which there may be spring in the
+pins, excess stress in some eye-bars due to inequalities of
+length, and a want of that rigidity peculiar to riveted structures,
+the deflection will be greater than above indicated for
+girders of the ordinary English type.</p>
+
+<p>The method in common use for measuring the deflections
+of girders but a moderate distance above the ground
+by means of sliding-rods, though crude, gives, with care,
+results sufficiently accurate for most practical purposes; but
+some points necessary to remember may be mentioned with
+propriety. The lower rod should rest firmly upon something
+solid, say a stone, well bedded and free from any tendency
+to rock; the upper end should bear against some part of
+the girder above, presenting a hard surface, free from dirt
+or scale, and as the running load approaches the bridge it
+should be ascertained that there is no slack, that the rods
+bear hard at the top and bottom. The upper end having
+been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other.
+These precautions are so self-evident that an apology is
+almost necessary for mentioning them.</p>
+
+<p>To ascertain deflections with a single pair of rods is only
+allowable when the girders rest firmly on their bearings; if<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span>
+felt has been placed under the girder ends, or if the bedstones
+are insecure or rocking, it is necessary to use three
+pairs of rods, one pair at the middle and a pair at each end,
+in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the
+desired result.</p>
+
+<p>In the case of a number of spans in series, each resting
+upon sill girders common to two sets of bearings, this
+method also gives results of indifferent reliability, as the
+depression of each end may be greater as the travelling load
+comes upon and leaves the span than when it is precisely
+over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular
+position of the running load, which are what is required.</p>
+
+<p>The author suggests, as a means of ascertaining deflections
+free from these objections, that it should be done by
+first measuring the slope at one end, and from this deducing
+the deflection at the centre.</p>
+
+<p>This is to be accomplished by means of a little instrument,
+consisting of a telescope with cross-hair sights, and
+fitted with a reflecting prism at the eye-piece capable of
+being turned round, so that the observer has a wide choice
+as to the position he assumes with reference to the instrument,
+and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one
+end of the girder over the bearing, at the other end a scale
+is secured, to which the telescope is directed, the cross hair
+being made to sight on the zero of the scale, or the reading
+noted. For a girder supposed to deflect to uniform curvature
+(say, with uniform depth and uniform stress, the
+ordinary case) the reading observed will be four times the
+deflection; every <sup>1</sup>&#8260;<sub>10</sub> inch actual reading on the scale will
+correspond to <sup>1</sup>&#8260;<sub>40</sub> inch of girder deflection.</p>
+
+<p>Apart from the deflection, this method gives a ready<span class="pagenum"><a name="Page_92" id="Page_92">[92]</a></span>
+means of observing the end slope, a quantity of equal value
+for purposes of comparison. As with girders of similar proportions,
+and similarly stressed, the deflection will at all
+spans be the same fraction of the span; so should the end
+slope be a constant quantity under similar conditions, the
+diagram, <a href="#Fig54">Fig. 54</a>, will make the principle quite clear.</p>
+
+<div class="figcenter"><a name="Fig54" id="Fig54"></a><a name="Fig55" id="Fig55"></a><a name="Fig56" id="Fig56"></a><a name="Fig57" id="Fig57"></a>
+<img src="images/illo104.png" alt="" width="350" height="429" />
+<p class="caption"><span class="smcap">Figs.</span> 54 to 57.</p>
+</div>
+
+<p>Strictly the character of the deflection curve is slightly
+modified by that part of the deflection due to the web; so
+that the depression at the centre would, in the case assumed
+above, be somewhat more than one-fourth part of the end
+reading, and generally will be a larger fraction of the reading
+than that deduced from a consideration of flange stress<span class="pagenum"><a name="Page_93" id="Page_93">[93]</a></span>
+simply. In <a href="#Fig55">Figs. 55 to 57</a>, which are intended to explain
+this, it will be noticed that deflection due to the web is
+shown straight-lined from the bearings to the centre of the
+girder; this is strictly true only for a girder correctly designed
+for an immovable distributed load; but as there
+should be for girders intended for a travelling load, some
+excess in web members near the centre under the condition
+of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as
+shown in the diagram for the sake of simplicity.</p>
+
+<p>Suitable constants, including the corrections necessary,
+are given in column A of the table annexed for a few typical
+cases, and by these constants the actual readings should be
+multiplied to find the deflection. The constants have been
+worked out for depths of one-tenth the span; for greater
+depths they should be slightly more, and for smaller depths
+somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly
+exceeding 5 per cent., and generally much less.</p>
+
+<p>The figures in column B relate to the formul&aelig; previously
+stated, and apply equally well to all depths.</p>
+
+<p class="center"><span class="smcap">Tables of Multipliers for Deflection.</span></p>
+
+<table summary="Table page 93">
+
+<tr>
+<td class="left padr3"><i>Uniform Stress</i>:</td>
+<td class="center padl1 padr1">A.</td>
+<td class="center padl1 padr1">B.</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3">Girders of uniform depth, varying flange section</td>
+<td class="center bot padl1 padr1">0&middot;27</td>
+<td class="center bot padl1 padr1">1&middot;00</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3">Hog-backed girders, ends half of centre depth, varying flange section</td>
+<td class="center bot padl1 padr1">0&middot;24</td>
+<td class="center bot padl1 padr1">1&middot;08</td>
+</tr>
+
+<tr>
+<td colspan="3" class="left padr3"><i>Varying Stress</i>:</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">[A]</a>Girders of uniform depth and flange section</td>
+<td class="center bot padl1 padr1">0&middot;32</td>
+<td class="center bot padl1 padr1">0&middot;87</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Hog-backed girders (as above), but uniform flange section</td>
+<td class="center bot padl1 padr1">0&middot;29</td>
+<td class="center bot padl1 padr1">0&middot;97</td>
+</tr>
+
+<tr>
+<td class="left top padl3 padr3"><a href="#Footnote_1" class="fnanchor">[A]</a>Bow-string girders of uniform flange section</td>
+<td class="center bot padl1 padr1">0&middot;16</td>
+<td class="center bot padl1 padr1">1&middot;30</td>
+</tr>
+
+</table>
+
+<div class="footnote">
+
+<p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">[A]</span></a> For uniform loading.</p></div>
+
+<p><span class="pagenum"><a name="Page_94" id="Page_94">[94]</a></span></p>
+
+<p>It is apparent that, if preferred, the scale, instead of
+being in inches, divided suitably, may, for each type of
+girder, be amplified to the proper degree, so that the amount
+of the deflection may be read off at once.</p>
+
+<p>This method of dealing with deflections is quite independent
+of the character of the bearings, and is applicable
+to girders at any height above ground or over water; but
+its use would hardly be practicable for very small beams, or
+those in an awkward position, or near which it would be
+impossible to remain with a running load upon the bridge.</p>
+
+<p>There is a possible source of error in the use of the
+instrument, most likely to occur with triangulated girders,
+with which, if the instrument is placed at the top of an end
+post, the reading observed may be the joint effect of deflection
+and of local flexure of the members meeting near the
+telescope. This may be tested, and, if necessary, allowed
+for, by first sighting upon a scale at the next apex, and
+observing the effect of the moving load. Again, as girders
+sometimes cant towards the running load, if the instrument
+is placed on one edge of a girder, and the cantings of the
+two ends are dissimilar, a false reading will result, which
+may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between
+the cants upon the observation. Only in exceptional cases
+is it likely that either of these considerations would need
+attention.</p>
+
+<p>The author has secured with this instrument very promising
+results, notwithstanding that under a running load there
+is a slight haziness of the scale as seen through the telescope,
+due to &#8220;dither,&#8221; largely the result of imperfections which
+may be remedied.</p>
+
+<p>Deflections may sometimes be conveniently taken, by a
+quick-eyed observer, with a good surveyor&#8217;s level and a
+specially-divided staff held at the centre of the girder. The
+divisions preferred by the author for this purpose are <sup>1</sup>&#8260;<sub>10</sub> inch,<span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span>
+plainly marked, which may be seen at 50 feet distance with
+sufficient clearness to make possible readings by estimation
+between the divisions to, say, <sup>1</sup>&#8260;<sub>50</sub> inch. But it is clearly
+desirable not to rely upon a single observation only, where
+all the evidence is gone so soon as the sight has been taken.</p>
+
+<p>In rail-bearers, or other short girders, it may not be
+practicable to adopt such methods, either on account of an
+inability to find a suitable place for the instrument, or to
+read with any telescope with sufficient promptitude as the
+load passes rapidly over. The use of rods may also be out
+of the question, as the errors attending their manipulation
+may be serious where but a small movement has to be noted,
+this being complicated in some instances by the bearings
+being insecure, and working to an extent which obscures the
+measurement sought. In such cases it is preferable to use
+a stiff slat lying along the girder, which bears, through
+short blocks over the girder bearings, upon the flanges; the
+deflection is then read by direct measurement of the girder&#8217;s
+depression at the centre, relative to the slat.</p>
+
+<p>The author is, unfortunately, not able to give any precise
+information on the effect of running-load as against a
+load that is stationary in connection with girder deflections.
+It is by no means easy in ordinary work upon a railway to
+secure facilities for making such comparative tests. It may,
+however, be confidently stated, as a result of such observations
+as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a
+50 feet span, but little greater than that due to the same
+load stationary; it may be, perhaps, 5 to 10 per cent. more.</p>
+
+<p>It is evident that to determine the precise difference
+where the quantity to be measured is so small needs apparatus
+of a more delicate character than that in common use,
+and the control of an engine, or engines, for the purpose of
+making the special tests, conditions which on a busy line can
+only be secured by special arrangements previously made.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_96" id="Page_96">[96]</a></span></p>
+
+<h2>CHAPTER IX.<br />
+<span class="chaptitle">DECAY AND PAINTING.</span></h2>
+
+<p>The author has collected particulars as to the amount and
+rate of rusting in metallic structures which are of some
+interest. In all such instances it is very necessary to note
+the conditions which have obtained during the process of
+wasting, as without this, misleading conclusions may be
+drawn. The information given relates in all cases to wrought
+iron, unless otherwise stated.</p>
+
+<p>A plate-girder bridge, having girders under rails, was
+found to be badly rusted. The atmospheric conditions were
+unusually trying, the air being damp and impregnated with
+acid fumes from adjacent steel works. That the wasting
+was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than
+those farther removed and partly sheltered from the corrosive
+influence.</p>
+
+<p>The webs were in places eaten right through, having
+lost a mean amount of about <sup>1</sup>&#8260;<sub>8</sub> inch full on each surface in
+twenty-eight years. Painting had not been well attended to.</p>
+
+<p>In a similar bridge, not a great distance from this, but
+sufficiently far away to modify the conditions for the better,
+considerable wasting was also observed, but more particularly
+where the girders had been built into masonry, which,
+loosening with the constant movement of the girder-ends,
+had allowed moisture to collect, and rust to develop, without
+the chance of repainting these surfaces. The amount of
+waste at the places indicated was, as in the last case, about<span class="pagenum"><a name="Page_97" id="Page_97">[97]</a></span>
+<sup>1</sup>&#8260;<sub>8</sub> inch on each face, and in the same time, other parts of
+the girders having suffered less.</p>
+
+<div class="figcenter"><a name="Fig58" id="Fig58"></a>
+<img src="images/illo109.png" alt="" width="350" height="60" />
+<p class="caption"><span class="smcap">Fig.</span> 58.</p>
+</div>
+
+<p>A third plate-girder bridge, with outer main girders,
+cross-girders, and plated floor, carrying a road over a railway
+and sidings, and which was known to have been
+neglected in the matter of painting, was very badly rusted,
+both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration
+was, however, the smoke and steam from locomotives, which
+frequently stood for some time, during shunting operations,
+directly under the bridge. The webs of the cross-girders,
+which were originally <sup>1</sup>&#8260;<sub>4</sub> inch thick, had rusted into occasional
+holes during fourteen years&mdash;i.e. <sup>1</sup>&#8260;<sub>8</sub> inch from each
+surface in that time. When removed a little later the
+wasting was so complete that it was possible to knock out
+with a light hammer the remains of the web between flanges
+and stiffeners, so as to leave an open frame only. One of
+the cross-girders was so treated by the men engaged upon
+the work, when it presented the appearance shown in <a href="#Fig58">Fig. 58</a>.</p>
+
+<p>In another case&mdash;that of a bridge with lattice girders
+under rails&mdash;the ends were built into masonry, which had,
+of course, loosened, with the usual result. The air of the
+locality was certainly pure, but somewhat damp. The general
+condition of the ironwork was good, but end-bars of the
+diagonal bracing, where they had been closed in, had lost
+<sup>1</sup>&#8260;<sub>8</sub> inch on each surface in thirty-three years. The top flanges
+immediately under the timber floor were in a very fair state,
+which is of some interest when it is considered that these<span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span>
+were made of steel of the same kind as that already noticed
+as being used in the construction of small girders (see <a href="#Fig46">Fig.
+46</a>, <i>ante</i>), described in the chapter upon &#8220;<a href="#Page_61">High Stress</a>,&#8221; both
+cases dating from the year 1861. The painting upon the
+lattice-girder bridge had been pretty well attended to; but
+in the case of the small steel girders it had been greatly&mdash;perhaps
+altogether&mdash;neglected; this, coupled with adverse
+atmospheric conditions, had produced the result that the
+rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully
+<sup>1</sup>&#8260;<sub>8</sub> inch on each surface, as against a negligible amount
+under the more favourable circumstances.</p>
+
+<p>Girder-work over sea-water, as in piers, seems to rust at
+a sensibly greater rate than inland work under average conditions;
+but it is hardly practicable to make any strict
+comparison, as in either case the rate of oxidation is so
+much affected&mdash;even controlled&mdash;by the care bestowed upon
+the structures. This general conclusion is based upon the
+results of examination of wrought-iron girder-work over sea-water
+of ages varying from fourteen to forty-four years. It
+should be remarked, however, that in one case steel girders
+but five years old, and which were frequently wetted with
+sea-spray, were found to be wasting rather badly&mdash;the paint
+refusing to keep upon the surface.</p>
+
+<p>It may be concluded from the above instances, and from
+others which have come under notice, that wrought-iron
+work, if not properly cared for in respect to painting, or
+under conditions otherwise bad, may be expected to rust at
+a rate which corresponds to the loss of <sup>1</sup>&#8260;<sub>8</sub> inch on each surface
+in from fifteen to thirty years; but with proper care as
+to painting, and exclusive of exceptionally bad conditions,
+it does not appear to waste at any measurable rate. In some
+instances, upon scraping the paint from girders which had
+been in use for thirty years, the author has found, beneath the<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span>
+original red lead, the metallic surface bright and clean,
+showing no trace of rust.</p>
+
+<p>Of ordinary steelwork the same cannot be said, the common
+experience being that mild steel is very liable to be
+attacked by rust. With passable care in the bridge-yard
+during manufacture, such that with wrought iron no after-trouble
+would be noticeable, steel is very liable to show,
+within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away
+discloses a small rust-pit. This is more often seen on the
+flange surfaces (horizontal) than on web surfaces (vertical),
+but it is probable the position has little to do with the
+matter, and that it is rather due to the fact that rust has
+been earlier started on the flange-plates, upon being put
+through the drilling-machines and inundated with slurry,
+which occurs only to a more limited extent with webs having
+fewer holes. The heads of steel rivets do not show this
+tendency to &#8220;pit,&#8221; or to early development of rust. The
+riveting is about the last operation in making a girder, each
+rivet being freed of all rust by heating, and quickly coming
+under the protection of oil or paint. It may happen in this
+way that the heads of rivets on a girder may be exposed
+without protection for as many hours only as the rest of the
+work for weeks, which fully accounts for the difference in
+behaviour.</p>
+
+<p>The essential point to be observed in all steelwork is to
+prevent, if possible, the first development of rust, for once
+begun it is much more difficult to arrest than in iron; for
+this reason, oiling of all material for a steel bridge, at a very
+early stage of its existence, cannot be too strongly insisted
+upon. This practice, however, makes the work so objectionable,
+and even dangerous when being lifted&mdash;because of the
+liability to slip&mdash;to the men engaged upon it, that it is
+commonly very difficult to ensure it being done sufficiently<span class="pagenum"><a name="Page_100" id="Page_100">[100]</a></span>
+soon to satisfy a careful inspector. If the work is carried
+out under cover, the requirement is less urgent. Strictly,
+all material should be oiled so soon as rolled, but the author
+does not remember to have seen this done at any of the
+mills he has visited, though it is common enough to find it
+specified.</p>
+
+<p>Ironwork does not need the extreme care which should
+be bestowed upon steelwork, but it is desirable that it should
+be painted as soon as possible, the surfaces being first
+thoroughly cleaned.</p>
+
+<p>There is, probably, for painting girder work nothing to
+beat good red lead as a protective coating; but there is considerable
+difficulty in getting it reasonably pure, without
+which quality its utility will be greatly reduced. The question
+of purity will, however, be found to be largely a question
+of price. It may be stated broadly that, whether for steel
+or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.</p>
+
+<p>In repainting old work, care should be taken to remove
+all traces of rust previous to laying on the new coat. It is
+not an altogether uncommon practice to repaint old structures
+by dealing only with the parts readily accessible, which,
+being less liable to rust, probably but little need it; leaving
+those parts which are difficult of access, and where rust is
+developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said,
+is indefensible. It is better rather to neglect the surfaces
+freely exposed and ventilated, and devote the whole care
+upon those other parts, confined and difficult to get at;
+taking the trouble necessary to remove ballast, timber, or
+whatever may obstruct the operation, in order that the bad
+places may be thoroughly scraped, and then painted. Those
+parts which most need attention may cost, perhaps, to reach&mdash;and
+deal with when exposed&mdash;ten times as much per yard<span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span>
+of surface as the rest of the superfices, which needs little,
+and is always accessible; but the cost should not deter the
+proper carrying out of the work, as it will prove the very
+worst sort of economy to deal with painting in a perfunctory
+manner.</p>
+
+<p>It should be noted that girder work, whether of wrought
+or cast iron, when embedded in lime or cement concrete, or
+mortar, generally proves to be very well preserved, provided
+that close contact has obtained. Cast-iron girders, when
+carrying jack arches resting upon the bottom flanges, are
+found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of
+new girders. Much the same remarks apply to girders of
+wrought iron carrying jack arches, where protected by the
+brickwork; provided that the girders are sufficiently stiff to
+minimise deflection, and allow the masonry or brickwork to
+adhere to the surfaces.</p>
+
+<p>Such girders are in a very different condition to those
+previously referred to, in which the ends of the girders,
+carrying a light floor structure, are built into masonry where
+the deflection slope is greatest; though, apart from the few
+cases where adherence can be relied upon, building-in is an
+undesirable practice, and has the disadvantage that after-examination
+is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted
+to.</p>
+
+<p>Cast iron has ordinarily&mdash;unlike wrought iron or steel&mdash;great
+capacity for resisting rust, and will, after many years
+of absolute neglect, appear but little the worse; an advantage
+which is the more pronounced when considered relatively
+to the greater thickness of the thinnest parts in
+cast-iron girders, the percentage of waste being proportionately
+lessened.</p>
+
+<p>Cast iron does, however, behave somewhat badly in sea-water,<span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span>
+the metal sometimes losing its original character, and
+becoming in time quite soft; though, if not worn away, as
+by the attrition of shingle, maintaining its original bulk.</p>
+
+<p>Of some forty-five cast-iron piles belonging to various
+structures, examined whilst engaged upon sea-pier work for
+Mr. St. George-Moore, though the author found somewhat
+diverse results, in no case did there appear to be any general
+softening of the whole thickness, but a distinct change for
+some definite distance inwards, generally to be decided without
+difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of
+softening was found close to the ground, this depth rapidly
+decreasing higher up, till, at a height of 5 feet, but little if
+any softening could be detected. At 2 feet above ground
+the softening was frequently but one-quarter of that at
+ground level. There was, too, often a considerable difference
+in the behaviour of different piles in the same structure
+under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly
+none at all. For six different structures the amount of
+softening near ground level, of about twenty-five piles
+examined, was as given in the table on the next page.</p>
+
+<p>The greatest depth of softening found (see No. 2) was
+<sup>9</sup>&#8260;<sub>16</sub> inch, 1 foot above ground, in a pile thirty-six years old.
+The decayed material when removed was of a soft, greasy
+consistency, perfectly black, which a few hours later was
+found to have changed to a dry yellow powder, by the rapid
+absorption, it may be supposed, of atmospheric oxygen. It
+is apparent, therefore, from this example that deterioration
+may proceed to a considerable depth; but it should be
+observed that other piles of the set showed softening at
+ground level of <sup>1</sup>&#8260;<sub>8</sub> inch only.</p>
+
+<p class="center"><span class="smcap">Softening of Cast-Iron Piles in Sea-Water.</span><span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span></p>
+
+<table class="nowrap" summary="Table page 103">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">No.</th>
+<th colspan="2" class="center padl1 padr1 br">Age.</th>
+<th colspan="2" class="center padl1 padr1 br">Maximum<br />Softening.</th>
+<th colspan="6" class="center padl1 padr1 br">Maximum<br />Rate of<br />Softening.</th>
+<th colspan="5" class="center padl1 padr1 br">Mean Rate<br />of<br />Softening.</th>
+<th class="center padl1 padr1 br">Quality<br />of<br />Metal.</th>
+<th class="center padl1 padr1 wrappable">Materials Entered<br />by Piles.</th>
+</tr>
+
+<tr>
+<td class="center top br">1</td>
+<td class="right top padl1">17</td>
+<td class="center top padr1 br">years</td>
+<td class="center top"><sup>5</sup>&#8260;<sub>16</sub></td>
+<td class="center top br">in.</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top padr0">7</td>
+<td>&nbsp;</td>
+<td class="center top padr1 br">years</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top">15</td>
+<td class="center top br">years</td>
+<td class="center top br">Soft</td>
+<td class="left top padl1 padr1 wrappable">Extremely soft sandstone.</td>
+</tr>
+
+<tr>
+<td class="center top br">2</td>
+<td class="right top">36</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>9</sup>&#8260;<sub>16</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">8</td>
+<td class="left top padl0"><sup>1</sup>&#8260;<sub>2</sub></td>
+<td class="center top br">&#8222;</td>
+<td colspan="5" class="center top br">No result</td>
+<td class="center top br">&#8222;</td>
+<td class="left top padl1 padr1 wrappable">Rubble mound.</td>
+</tr>
+
+<tr>
+<td class="center top br">3</td>
+<td class="right top">32</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>3</sup>&#8260;<sub>8</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">11</td>
+<td>&nbsp;</td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">in.</td>
+<td class="center top">in</td>
+<td class="right top">15</td>
+<td class="center top br">years</td>
+<td class="center top padl1 padr1 br wrappable">Moderately hard</td>
+<td class="left top padl1 padr1 wrappable">Fine sand.</td>
+</tr>
+
+<tr>
+<td class="center top br">4</td>
+<td class="right top">38</td>
+<td class="center top br">&#8222;</td>
+<td class="center top"><sup>1</sup>&#8260;<sub>10</sub></td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top padr0">47</td>
+<td>&nbsp;</td>
+<td class="center top br">&#8222;</td>
+<td class="center top padl1"><sup>1</sup>&#8260;<sub>8</sub></td>
+<td class="center top">&#8222;</td>
+<td class="center top">in</td>
+<td class="right top">140</td>
+<td class="center top br">&#8222;</td>
+<td class="center top br">Hard</td>
+<td class="left top padl1 padr1 wrappable">Extremely hard rock.</td>
+</tr>
+
+<tr>
+<td class="center top br">5</td>
+<td class="right top">17</td>
+<td class="center top br">&#8222;</td>
+<td colspan="2" class="center top br">Small</td>
+<td colspan="6" class="center top padl1 padr1 br">Negligible</td>
+<td colspan="5" class="br">&nbsp;</td>
+<td class="center top br">(?)</td>
+<td class="left top padl1 padr1 wrappable">Sand and Shingle.</td>
+</tr>
+
+<tr class="bb">
+<td class="center top br">6</td>
+<td class="right top">14</td>
+<td class="center top br">&#8222;</td>
+<td colspan="2" class="center top padl1 padr1 br">Negligible</td>
+<td colspan="6" class="center top br">Ditto</td>
+<td colspan="5" class="br">&nbsp;</td>
+<td class="center top br">(?)</td>
+<td class="left top padl1 padr1 wrappable">Sand.</td>
+</tr>
+
+</table>
+
+<p>The least rate of softening noticed, apart from those
+structures of a more recent date, in two of which it was<span class="pagenum"><a name="Page_104" id="Page_104">[104]</a></span>
+very slight, occurred in a pier thirty-eight years old (No. 4),
+where, of three piles tested, two were quite hard, and the
+third softened <sup>1</sup>&#8260;<sub>10</sub> inch only.</p>
+
+<p>Whatever may be the precise cause of the change, it
+does not appear to be affected by the period or percentage
+of immersion during the rise and fall of tides.</p>
+
+<div class="figcenter"><a name="Fig59" id="Fig59"></a>
+<img src="images/illo116.png" alt="" width="500" height="397" />
+<p class="caption"><span class="smcap">Fig.</span> 59.</p>
+</div>
+
+<p>This will be clear from the diagram, <a href="#Fig59">Fig. 59</a>, which
+refers to four piles (No. 3 of table), all of the same age, in
+the same structure. On each pile the depth of softening is
+given at points in strict relation to each other, and to the
+tidal range. The percentages of immersion for the various
+heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening;
+this, indeed, is always greatest near the ground, at
+whatever actual height it may be. For instance, pile A was<span class="pagenum"><a name="Page_105" id="Page_105">[105]</a></span>
+at ground-level softened <sup>1</sup>&#8260;<sub>4</sub> inch, that point being 60 per
+cent. of its life under water; but on pile B, at a point 74
+per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level
+of this pile, the percentage being there 87, the softening
+was no greater than at ground-level at pile A.</p>
+
+<p>It is probable that while the percentage of submersion
+in moving water hardly appears to affect the result, yet prolonged
+contact with wet sand, sea-weed, or clinging shell-fish
+may do so. This seems to suggest that the process of change,
+as between the sea-water and the iron, is slow, and to be
+effective must be continuous; so that it is only found to
+any considerable extent where the water in contact with the
+surface is still. In the two worst cases, Nos. 1 and 2 of the
+table, at points 1 foot and 6 inches above ground-level,
+the surface was in one pile shrouded in a thick mantle of
+heavy sea-weed, and in the other covered by molluscs; in
+both instances the surfaces being thus kept moist and undisturbed.
+The piles of the fourth case were in hard rock,
+were clean, and, where accessible, always either in moving
+water or quite dry.</p>
+
+<p>However this may be, the power to resist softening
+certainly appears to vary largely with the quality of the
+iron. The piles, referred to above, in which deterioration
+proceeded at the most rapid rate were certainly of a soft
+metal, the first being markedly so. On the other hand,
+certain piles (No. 4) of hard, close-grained iron suffered very
+little.</p>
+
+<p>It may be mentioned with respect to the last named, as
+a matter of interest, that the caps of the lower lengths (just
+above ground-level) had been cast with short pieces of
+wrought iron projecting&mdash;possibly for lifting purposes&mdash;which
+during thirty-eight years had altered in character to
+something very like softened cast iron, but laminated, and<span class="pagenum"><a name="Page_106" id="Page_106">[106]</a></span>
+harder. Of about 1<sup>1</sup>&#8260;<sub>4</sub> inch original thickness, only <sup>3</sup>&#8260;<sub>16</sub> inch
+remained having the semblance of wrought iron. The
+percentage of submersion was about 60.</p>
+
+<p>A number of piles, not included in the table, varying
+from fifteen to forty-four years old, and of the same structure
+to which set No. 2 belonged, were all found to be hard,
+with the exception of one showing <sup>3</sup>&#8260;<sub>16</sub> inch of softening.
+These are omitted, because the mud surrounding them was
+at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points
+testing might have disclosed different results. It is probable
+that for any piles standing in soft material examination
+below the surface would reveal more pronounced softening
+than where occasionally exposed.</p>
+
+<p>To meet the effects of sea-water on cast-iron piles, and
+for other reasons, it is a common and good practice to make
+the lower lengths of greater thickness&mdash;say, <sup>3</sup>&#8260;<sub>8</sub> inch more&mdash;than
+that sufficient for the upper. Occasionally, also, the
+bottom lengths are filled with concrete, which no doubt adds
+to the length of time during which they may be relied upon.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span></p>
+
+<h2>CHAPTER X.<br />
+<span class="chaptitle">EXAMINATION, REPAIR, AND STRENGTHENING OF
+RIVETED BRIDGES.</span></h2>
+
+<p>In the preceding chapters defects of various kinds to which
+riveted bridgework is liable have been more particularly
+dealt with; it is now proposed to consider the examination
+of such structures, following this by a reference to methods
+of repair and strengthening, leaving the treatment of other
+classes of bridgework to be developed under their proper
+headings, though some of the remarks immediately following
+will apply to all.</p>
+
+<p>The exhaustive survey of a bridge is only to be made
+after considerable experience in the work, but it may be
+stated that in looking for defects it is well to seek where they
+are least expected, till, with practice, one knows better where
+to direct attention. When examining with a view to pronouncing
+an opinion upon the fitness of the structure to
+remain in place, if in any real doubt, it is wise to give a
+casting vote against it; and finally it may be said that upon
+taking down a bridge condemned for any one or more defects,
+it should be examined for worse. This may seem to be
+somewhat pessimistic, but is based upon the teachings of
+experience.</p>
+
+<p>Preliminary examination of a bridge may reveal such
+faults or weaknesses as at once to ensure its condemnation;
+but if this is not the case, and there is a reasonable probability
+that the structure may be given a fresh lease of life,
+it will, for the purpose of estimating the strength, or for<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span>
+possible repairs, commonly be desirable to secure precise
+particulars of the existing structure independently of any
+drawings that may be in existence, and which will very
+probably be incorrect, the finished work, if old, seldom
+agreeing with the contract drawings. A final decision may in
+this case be deferred till after the measuring up has been
+completed, the condition of the structure becoming more
+familiar in the process.</p>
+
+<p>It is desirable first to ascertain whether the bridge
+remains in good form, whether the camber of girders appears
+to be what might be expected, or agreeable with existing
+records, though much reliance must not be placed upon
+figured cambers, it being quite common for girders to leave
+the bridge yards with the camber something other than
+that intended. The deflections under live load will also be
+observed, and compared with the calculated result, or checked
+by judgment. The calculations upon which strength and
+deflections are based will, of course, refer to the actual
+sections, which are sometimes a little difficult to ascertain if
+there has been irregular rusting. In continuous girders also,
+levels having been taken, allowance should be made for
+effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the
+like object. It is seldom that the main flanges of girders
+show signs of weakness, unless from flexure in the case of
+long and narrow top members, insufficiently stiffened; but
+there may be want of truth from other causes already dealt
+with. In plate girders the webs should be most carefully
+scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange
+angles, if the floor rest upon the flange. All riveted connections,
+of course, need close attention, both for straining
+effects, where there is a liability to wracking, and to detect
+loose rivets. Loose rivets and want of tightness in other<span class="pagenum"><a name="Page_109" id="Page_109">[109]</a></span>
+parts of the work may frequently be detected at sight by a
+reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects
+of weather; it may be seen round rivet-heads or along the
+edges of angle-bars, or other parts where there is movement.
+Loose rivets, though generally to be detected also by the
+hammer, may perhaps in the case of thin-webbed cross-girders
+be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may
+sometimes be detected by simultaneous deflection tests&mdash;with
+rods&mdash;at the top and bottom flanges of a girder, at the same
+distance from the bearings. Any difference in the readings
+may indicate loose web-rivets, or possibly a tear in the web
+running parallel to the flange angles.</p>
+
+<p>Bracings between girders are very apt to display a rich
+harvest of working rivets. Cross-girders and longitudinals
+also may have loose rivets at their connections, and be very
+badly wasted, with quite possibly cracks in the webs, or
+other defects already enlarged upon.</p>
+
+<p>The condition of the road upon the bridge will frequently
+be an indication of the state of the floor which carries it; or
+the existence of rail-joints which are working badly may
+very properly lead to a critical examination of the girder-work
+immediately below, as this is a fruitful source of
+damage in light constructions. Floor-plates, where these
+exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the
+latter being often loose and unsatisfactory.</p>
+
+<p>Trough floors may be expected to show loose rivets near
+the ends, with a probability of excessive leakage where they
+abut against the webs of supporting girders.</p>
+
+<p>Floor plates resting upon abutments or piers, being very
+liable to serious decay, require attention, and girder-work
+entering masonry should receive close scrutiny, any obstruction<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span>
+to a sufficient examination being removed so far as is
+judged sufficient for the purpose. The structure should, of
+course, be closely watched during the passage of live load
+for any signs of abnormal movement, excessive vibration, or
+lurching.</p>
+
+<p>In addition to seeking for these various defects, or others
+which have been referred to in these pages at length, it
+will be well always to be alive to the possibility of faults
+to be seen for the first time, or of which the author has
+furnished no instance.</p>
+
+<p>Having formed a reliable opinion as to the state of the
+bridge, this, if satisfactory, may leave to be determined only
+the question of strength relative to the loads carried. It is
+apparent that stress limits suitable for a new structure,
+which has all its life before it, of purpose moderate to cover
+possible deteriorations, the growth of loads, and other adverse
+influences, may to avoid immediate reconstruction, reasonably
+be permitted of a higher value for a further term of
+years in the case of a structure which it is known has for a
+considerable period behaved well, and remains in good condition.
+What this higher value may be will be greatly
+influenced by the circumstances of each case, and, being
+largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the
+nominal unit stress in an old bridge may be a very considerable
+amount in excess of that allowed for new work,
+without, of necessity, showing any ill effects; and the author
+is of opinion that for old bridges in good condition it is
+quite prudent to allow an excess of 33 per cent. beyond that
+permissible for a new design. If the structure is too weak
+to satisfy this modified condition, it may be possible to
+bring it within the stress limit by a reduction of ballast or
+other removable dead weight. If this expedient does not
+promise to be satisfactory, or the bridge shows actual signs of<span class="pagenum"><a name="Page_111" id="Page_111">[111]</a></span>
+weakness, or palpable defects, it will be necessary to deal with
+the question of repair, strengthening, or reconstruction.</p>
+
+<p>The repair of built up bridgework resolves itself largely
+into a matter of replacing loose rivets by cutting these out,
+rhymering the holes, if desirable, and again riveting. It
+will often be sufficient to do this with no particular precautions
+as to bolting up temporarily; the rivets having been
+loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to
+remove all the rivets, bolting up securely as this is done, in
+order to make a tight job, taking out each bolt in turn as
+required, and again filling the holes; or it may be well in a
+bad case first to remove all loose rivets, substituting good
+bolts, in order that work which has gone out of shape owing
+to defective rivets may first be brought true.</p>
+
+<p>Cross-girder webs, cracked vertically or nearly so, are
+commonly repaired with splice-plates on either side; but in
+doing this it is undesirable to add plates of excessive thickness
+relative to the web&mdash;probably poor&mdash;as by an abrupt
+change of web section it appears not unlikely a fresh break
+may be favoured.</p>
+
+<div class="figc450"><a name="Fig60" id="Fig60"></a><a name="Fig61" id="Fig61"></a><a name="Fig62" id="Fig62"></a><a name="Fig63" id="Fig63"></a>
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 60.</span> <span class="right49"><span class="smcap">Fig.</span> 61.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 60. and <span class="smcap">Fig.</span> 61.</p>
+<img src="images/illo124.png" alt="" width="450" height="376" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 62.</span> <span class="right49"><span class="smcap">Fig.</span> 63.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 62. and <span class="smcap">Fig.</span> 63.</p>
+</div>
+
+<p>Replacing wasted flange-plates, or adding new plates to
+those which exist, is occasionally resorted to in the case of
+main girders, the flanges of which are sufficiently accessible,
+but the operation is difficult, takes some little time, and
+should only be attempted under the constant supervision of
+a thoroughly capable man. When done, if the girder has
+not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the
+new section, the old always taking more by the amount of
+the dead-load stress previously carried. The method which
+the author has seen applied to lattice girders of about
+80 feet span, having good angle-bars in the flanges, with a
+shallow vertical web for attachment of diagonals, consisted<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span>
+in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been
+removed. The new plate length having been prepared, was,
+on a Sunday, during a few hours&#8217; cessation of traffic, marked
+off, the temporary bolts being removed for the purpose, and
+then replaced. After the plate had been drilled, on a later
+Sunday, it was finally put into position, bolted up, and
+riveted at leisure; cover-plates make additional trouble, but
+are dealt with on the same principle. The method as shown
+in <a href="#Fig60">Fig. 60</a> is, however, barely practicable for so many plates.
+It is preferable, if it is proposed to add section, to do this
+with as little interference as possible with existing rivets of
+importance. This may be accomplished, if the existing
+plates are not too wasted at their edges, by riveting on new
+strips or angle-bars (see <a href="#Fig61">Figs. 61 to 63</a>). Occasionally the
+strength of a girder is increased by the addition to the top<span class="pagenum"><a name="Page_113" id="Page_113">[113]</a></span>
+or bottom boom of material in such a form as sensibly to
+increase the depth, and thus, while adding increased section
+to one boom, to reduce the stress in each, though to dissimilar
+amounts. By this device also the relief is effective
+only as regards the live-load stress; under dead load only
+the new material does no work, provided, of course, that
+no relief staging was used during the alterations. For
+girders carrying any considerable proportion of dead load the
+method is very inefficient, though for others, in which the
+live load is relatively large, the result should be more satisfactory.</p>
+
+<p>As this question of adding new section to old is of much
+importance in dealing with repairs and strengthening operations,
+a few general remarks upon the subject will be
+pertinent. The difficulty in such work commonly is to
+cause the new to render any considerable assistance to the
+old in those cases which occur in practice. If a bar be
+imagined under longitudinal stress varying between 0 and a
+maximum, then, if the area of the piece be increased at the
+time when it takes no stress, its capacity for resisting the
+maximum amount will be increased, and for added material
+of similar elasticity the unit stress proportionately reduced.
+If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any
+degree. To take a third case, of the maximum being twice
+the minimum load, it will be necessary, in order to lower the
+maximum unit stress by 25 per cent., to double the original
+section of the bar if, as supposed, the extra metal has been
+added to the piece when under the smaller load, so that the
+new section is only effective in assisting to carry the remainder
+of the load at such times as it may be imposed.
+The relationship stands thus<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><span class="division"><span class="num">Live load</span><span class="denom">Live + dead load</span></span> &times; <span class="division"><span class="num">New area</span><span class="denom">New + old area</span></span> = relief.</p>
+
+<p><span class="pagenum"><a name="Page_114" id="Page_114">[114]</a></span></p>
+
+<p>These statements will be true under the conditions named,
+within the elastic limit of the material; but some advantage
+would be derived in the second case, and a more marked
+benefit in the third, if the load assumed to be a maximum
+were exceeded, or if the composite bar were tested to destruction;
+as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment
+as to how far this reserve of strength may be considered of
+value.</p>
+
+<p>If, instead of simply adding section to the bar, some part
+of the constant load is put upon the new section by the
+manner of attachment, the combination will, of course, be
+more effective.</p>
+
+<p>To apply these considerations and illustrate the way in
+which the two methods of adding flange section work out
+when reduced to figures, the case will be supposed of a girder
+6 feet deep, carrying a load of which one-third is dead and
+two-thirds live. To the flanges of this girder are added
+plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the
+girder before strengthening is liable, the depth remaining
+substantially unaltered. With dead load only the original
+section would be stressed to 2&middot;3 tons per square inch, the
+new section being then unstressed. Under full load the
+new and old material take 3&middot;1 tons per square inch additional,
+making the modified stress on the original section
+5&middot;4 tons per square inch, as against 7 tons; or a reduction
+of 22 per cent. This compares with 33 per cent., the relief
+due to 50 per cent. increase of flange area under ordinary
+conditions of stress distribution.</p>
+
+<p>Let the second method of strengthening the girder now
+be considered, using, for purposes of comparison, the same
+total amount of new material to increase the girder depth by
+an addition to the top flange. This section will be equal to<span class="pagenum"><a name="Page_115" id="Page_115">[115]</a></span>
+the area of one flange, which, though it may be applied in
+many different ways, giving a greater or a less increase to the
+depth, would probably be used in some
+such manner as that shown in <a href="#Fig64">Fig. 64</a>,
+increasing the effective depth for live-load
+stress by nearly 10 inches.</p>
+
+<div class="figcenter"><a name="Fig64" id="Fig64"></a>
+<img src="images/illo127.png" alt="" width="125" height="494" />
+<p class="caption"><span class="smcap">Fig.</span> 64.</p>
+</div>
+
+<p>The added material will, as in the
+previous case, leave the dead-load stress
+unaltered, or 2&middot;3 tons per square inch.
+The stress in the bottom flange due
+to live load will, however, now be 4&middot;1
+tons per square inch, making a total
+stress of 6&middot;4 tons per square inch,
+against 7 tons&mdash;the original stress.
+The reduction here is 8 per cent.
+only, as compared with 12 per cent.,
+the relief due, under ordinary conditions,
+to an increase of effective depth
+from 6 feet to 6 feet 10 inches, and by
+the use of additional material, equal,
+as before, to one-half of the total
+flange areas before the alteration.</p>
+
+<p>The effect on the top flange need
+not be here gone into in detail, but it
+may be said that, owing to the increase
+of gross section and of depth,
+the ultimate stresses of both the new
+and old material are greatly less than
+as given for the bottom flange.</p>
+
+<p>Girders strengthened by the first
+of these two methods would, it is probable,
+if tested to destruction, give
+results more nearly in accord with the actual percentage
+increase of flange section, plastic deformation of the metal,<span class="pagenum"><a name="Page_116" id="Page_116">[116]</a></span>
+before failure, tending to reduce the differences of stress on
+the new and old material of the sections.</p>
+
+<div class="figcenter"><a name="Fig65" id="Fig65"></a><a name="Fig66" id="Fig66"></a>
+<img src="images/illo128.png" alt="" width="350" height="470" />
+<p class="caption"><span class="smcap">Figs.</span> 65 and 66.</p>
+</div>
+
+<p>Web members of lattice girders may, if weak, sometimes
+be dealt with by the introduction of supplementary bars,
+parallel to and between the old members, or by the addition
+of strips or angles to the existing diagonals. The treatment
+will be largely influenced by the nature of the old detail,
+which may lend itself to some one arrangement much better
+than to any other.</p>
+
+<p>End riveting of web members may, if it has become
+loose, be dealt with by simply rhymering the holes a size
+larger, and re-riveting in the best manner, if the stresses are
+not excessive; or it may be necessary to devise some additional
+attachments by which new rivets are brought into use
+(see <a href="#Fig65">Figs. 65 and 66</a>). The effective relief due to supplementary<span class="pagenum"><a name="Page_117" id="Page_117">[117]</a></span>
+rivets will be influenced by similar considerations
+to those governing increase of section.</p>
+
+<div class="figcenter"><a name="Fig67" id="Fig67"></a>
+<img src="images/illo129.png" alt="" width="450" height="251" />
+<p class="caption"><span class="smcap">Fig.</span> 67.</p>
+</div>
+
+<div class="figcenter"><a name="Fig68" id="Fig68"></a>
+<img src="images/illo130.png" alt="" width="450" height="264" />
+<p class="caption"><span class="smcap">Fig.</span> 68.</p>
+</div>
+
+<p>Old structures are very frequently deficient in bracing,
+which may, in such cases, be advantageously introduced;
+or girders individually weak may be rendered collectively
+efficient by suitable bracing. In considering the advisability
+of this, however, the case should be viewed with regard to
+the possible effects of such members, as already dealt with
+in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders
+may have the effect, under live load, of increasing the stress
+on the outer girders due to twisting of the structure as a whole,
+though the inner girders will, except for full loading of the
+whole bridge, be advantaged as to stress values, and in any
+event bettered by being held up to their work. The effect
+upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations
+the detail should be schemed with special care to
+ensure simplicity in execution, smith&#8217;s work being rigorously
+avoided. A good arrangement for supplementary bracing
+between plate-girders, which gives little trouble in carrying
+out, is shown in <a href="#Fig67">Fig. 67</a>; or where the stiffeners of such girders<span class="pagenum"><a name="Page_118" id="Page_118">[118]</a></span>
+are in line across the bridge, the detail given in <a href="#Fig68">Fig. 68</a> may
+involve less expenditure. Difficulties may be experienced in
+riveting, unless great care is taken in the positioning of rivets.
+Fitting-bolts are only to be relied upon as such, if they really
+justify the name; they are, though easy to specify, by no
+means easy to secure under the conditions of practical work.
+Weak cross-girders may make alterations&mdash;in some cases
+considerable&mdash;necessary, to rectify the defect of strength.
+The removal of old girders to make room for new is seldom
+resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders
+between the old in cases where there is no plated floor to
+make the work difficult. By this method there is, of course,
+an increase of appreciable amount in the dead load carried
+by the main girders, which would in many instances be
+objectionable. With deep and heavy main girders, having
+plate webs, cross-girders may be strengthened by improving
+the end connections by suitable gussets, and attachment to
+good vertical stiffeners, the fixity of the ends thus aimed at
+being assured by overhead struts or girders, from one main
+girder to its fellow, at intervals apart well considered with
+reference to the horizontal strength of the top flanges, the<span class="pagenum"><a name="Page_119" id="Page_119">[119]</a></span>
+whole thus making a closed frame, as shown in <a href="#Fig69">Fig. 69</a>.
+The method appears feasible, but it should be stated that
+the author has not known it to be applied in its entirety as
+a means of strengthening an old floor.</p>
+
+<div class="figcenter"><a name="Fig69" id="Fig69"></a>
+<img src="images/illo131.png" alt="" width="450" height="280" />
+<p class="caption"><span class="smcap">Fig.</span> 69.</p>
+</div>
+
+<p>A simple and very common device consists in substituting
+for the ordinary cross-sleeper road, where this exists, stout
+timber longitudinals under the rails, which have, where the
+cross-girders do not exceed 5 feet centres, a marked distributive
+effect, tending to reduce the maximum load upon any
+individual girder. With a similar object, trough girders
+containing longitudinal timbers are sometimes adopted where
+the depth available is not enough to enable sufficiently stiff
+timbers to be used alone. In either case the object sought
+is the same&mdash;to modify the effect of the heavier wheel loads
+upon isolated cross-girders. When the spacing is so close
+as 4 feet, the beneficial result of this treatment is considerable,
+but at 8 feet centres it can have but a moderate effect
+where timbers alone are used.</p>
+
+<p>Occasionally, for long cross-girders, a distributing girder
+is placed, with the same intent, in the 6 feet way, its function
+being limited to this use only if the depth and strength are<span class="pagenum"><a name="Page_120" id="Page_120">[120]</a></span>
+sufficiently small to serve this object alone, as distinct from
+the case in which it becomes a carrying girder transferring
+load to the abutments. As a distributor simply, the girder
+has to equalise the bending moments amongst the cross-girders,
+to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous
+to alteration, for a position of the wheel loads such that the
+heaviest comes upon a centre cross-girder, the mean of these
+moments will, when compared with that for each girder,
+show the difference to be induced as a result of introducing
+the distributor. These differences of moment render necessary
+at the centre of the cross-girders reactions upwards
+or downwards, as the case may be, of amounts competent
+to induce moments below the inner rails equal to these
+differences.</p>
+
+<p>It is these reactions which must be provided by the distributing
+girder at a moderate stress, and without flexure of
+such an amount as sensibly to modify the reactions. The
+greatest section necessary at any one point may then be
+adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no
+harm in a little excess in a case of this kind, the total cost
+being but little affected by some small addition to the weight,
+where labour upon the site is so considerable an item as in
+work of this description. The ends of the distributing girder
+should be carried on to the abutments or piers to ensure
+adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at
+an early stage, by boning or by levelling, the condition of
+the cross-girders as to uniformity of heights, as this may affect
+the length most suitable for separate sections. Between the
+underside of the distributor and the cross-girder tops there
+will commonly be spaces of varying amounts, which should
+be filled by packings to fit, rather than by pulling the work<span class="pagenum"><a name="Page_121" id="Page_121">[121]</a></span>
+together by force, introducing undesirable stresses of uncertain
+amount.</p>
+
+<p>In the earlier remarks upon the strengthening of bridgework
+by the use of new material, it has been assumed that
+the modulus of elasticity of the new metal is similar to that
+of the old; it may, however, as in cases where wrought-iron
+work is reinforced by additions in steel, be necessary to
+take the difference of elastic properties into account, with
+which object the new section should be multiplied by a
+quantity (greater or less than unity) inversely proportional to
+the higher or lower modulus of the new material, that is to
+say, by</p>
+
+<p class="formula"><span class="division"><span class="num">E of old material</span><span class="denom">E of new material</span></span></p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span></p>
+
+<h2>CHAPTER XI.<br />
+<span class="chaptitle">STRENGTHENING OF RIVETED BRIDGES BY CENTRE
+GIRDERS.</span></h2>
+
+<p>The addition of distributing girders, described in the last
+chapter, as a means of strengthening a bridge floor, while
+sufficient in many cases so far as the cross-girders are concerned,
+does not in any appreciable way assist the main
+girders. When for a two-line bridge, having outer main
+girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders
+may be used, placed either above or below the cross-girders,
+on the centre line of the bridge.</p>
+
+<p>There are two principal ways in which such a girder may
+be brought into use; the easier, but generally less economical,
+is by making a simple attachment to the cross-girders,
+the old girder work still taking the whole dead load. By this
+method the new girder does no work but carry itself till the
+live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the
+second method is to make the connection adjustable, so that
+a part of the floor weights may be imposed upon the new
+girder as an initial load. In doing this the old outer girders
+will rise slightly, being relieved of stress, and the cross-girders
+also lifted at the middle, whilst the new girder is
+depressed as the load is brought upon it. With some part
+of the live load a very considerable proportion of the total
+may in this way be carried by a centre girder of moderate
+section. The whole question, by either method, turns upon<span class="pagenum"><a name="Page_123" id="Page_123">[123]</a></span>
+deflections; and it is in determining the relative movements
+of the girders that the problem chiefly lies.</p>
+
+<p>It is convenient first to determine the percentage of load
+relief to be effected in the main girders, as to which it is to
+be observed that as this relief (distributed) is induced by
+the upward reaction of the new girder acting at the centre
+of the cross-girders, the stress relief of these will, as a rule,
+greatly exceed that of the outside girders. For the generality
+of cases, it may be taken that the relief suitable for the
+outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress
+in these to a greater degree.</p>
+
+<p>If, however, it be thought desirable to check this, it may
+be done by considering a cross-girder subject to its dead and
+live loads acting downwards, and to reactions at the centre
+and ends. At the centre the reaction will be the load of
+which the two main girders are relieved on a length equal to
+the pitch of the cross-girders, or as here given<span class="nowrap">:&mdash;</span></p>
+
+<p class="numform"><a name="Form1" id="Form1"></a><span class="formula"><i>c</i> &times; <i>t</i> &times; P = reaction at centre</span>
+<span class="number">(1)</span></p>
+
+<p><i>c</i> being the percentage of relief; <i>t</i> the total load per foot run
+of the bridge; and P the pitch of cross-girders. The live
+loads carried by the cross-girders are for this purpose taken
+at per foot run, as for the main girders. With these data
+it will be easy to construct a diagram of moments, making
+it evident whether the relief proposed for the main girders
+will give a sufficient percentage of relief to the floor beams.</p>
+
+<p>Granting that this proportion has been decided, and
+dealing first with the case in which the centre girder is
+simply attached to the cross-girders, and takes no dead load
+other than its own weight, then the live load carried by the
+outside girders, and previously borne wholly by them, will
+be reduced by the amount it is intended to transfer to the
+centre girder, and will become</p>
+
+<p class="numform"><a name="Form2" id="Form2"></a><span class="formula">L<sub class="lg"><i>l</i></sub> - (<i>c</i> &times; L<sub class="lg"><i>t</i></sub>) = live load on outer girders</span>
+<span class="number">(2)</span></p>
+
+<p><span class="pagenum"><a name="Page_124" id="Page_124">[124]</a></span></p>
+
+<p>L<sub class="lg"><i>l</i></sub> being the total live load, and L<sub class="lg"><i>t</i></sub> the total dead and live
+load carried by the bridge. From this the deflection of the
+outer girders corresponding to this modified live load may
+be derived.</p>
+
+<div class="figcenter"><a name="Fig70" id="Fig70"></a>
+<img src="images/illo136.png" alt="" width="550" height="251" />
+<p class="caption"><span class="smcap">Fig.</span> 70.</p>
+</div>
+
+<p>It is next necessary to ascertain the vertical movement,
+commonly a depression, of the cross-girders at the centre
+relative to their ends, when subject to the running load only,
+and supported at the middle and ends, the centre reaction
+being obtained as before indicated <a href="#Form1">(1)</a>. This movement
+will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the
+upward flexure of the girder due to the centre reaction,
+considered as separate effects. Stress values having been
+estimated for the two conditions, these results may readily
+be deduced by simple flexure formul&aelig;, observing that while
+the curve of moments due to live load sufficiently approximates
+to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter
+&#8220;<a href="#Page_85">Deflections</a>,&#8221; the flexure due to the centre reaction will be
+but 0&middot;80 of that which corresponds to the same stress for
+distributed loading. Or, the curve assumed by the girder
+under live load may be plotted by a method to be later
+explained.</p>
+
+<p><span class="pagenum"><a name="Page_125" id="Page_125">[125]</a></span></p>
+
+<p>The sum of the movements now determined&mdash;that is,
+the live-load deflection of the outer girders, and depression,
+as is commonly the case, of the cross-girders&mdash;will give the
+extreme depression (marked <i>m</i> in <a href="#Fig70">Fig. 70</a>), from the dead-load
+condition of the middle cross-girders, when supported
+to the extent desired by a centre girder whose proportions are
+not yet known, but which, carrying the required percentage
+of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the
+flanges of the new girder, governed by this flexure, will for
+a plate girder be</p>
+
+<p class="numform"><a name="Form3" id="Form3"></a><span class="formula"><span class="division"><span class="num">D &times; C &times; <i>m</i></span>
+<span class="denom">S<sup>2</sup></span></span> = <i>f</i>, unit stress on gross section</span>
+<span class="number_up">(3)</span></p>
+
+<p>D and S being, as before (see &#8220;<a href="#Page_85">Deflections</a>&#8221;), the depth and
+span respectively in feet, C a constant, <i>m</i> the deflection in
+inches, and <i>f</i> the stress per square inch on the gross section
+of flange.</p>
+
+<p>The gross area A, of the flange, is given by</p>
+
+<p class="numform"><a name="Form4" id="Form4"></a><span class="formula"><span class="division"><span class="num">S &times; <i>c</i> &times; L<sub class="lg"><i>t</i></sub></span>
+<span class="denom">8 &times; D &times; <i>f</i></span></span> = gross area of flange</span><span class="number_up">(4)</span></p>
+
+<p><i>c</i> &times; L<sub class="lg"><i>t</i></sub>, being, as in <a href="#Form2">(2)</a>, the load transferred to and carried
+by the centre girder.</p>
+
+<p>The actual stress in the flanges will, of course, be greater
+by an amount due to the girder&#8217;s own weight; but this does
+not affect the question of relief. For any ordinary case the
+stress per square inch will be low; but it will manifestly be
+useless to assume a greater stress with a view to economy, as
+the effect of reducing the section will simply be to make the
+girder too flexible, thus causing it to be less effective than
+primarily intended. If, as is seldom the case, there is
+freedom as to the depth of girder permissible, it is evident
+the unit stress may be made a condition, and the depth<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span>
+deduced by a suitable modification of formula <a href="#Form3">(3)</a>; the
+relief desired being in this way equally well assured. Indeed,
+in the rare instances in which any depth may be
+adopted, this method is&mdash;contrary to the general rule&mdash;distinctly
+economical, particularly if the girder may be placed
+below the cross-girders, which simply rest upon it, without
+elaborate attachments.</p>
+
+<div class="figcenter"><a name="Fig71" id="Fig71"></a>
+<img src="images/illo138.png" alt="" width="550" height="259" />
+<p class="caption"><span class="smcap">Fig.</span> 71.</p>
+</div>
+
+<p>Considering now the second method of applying centre
+girders by which the new girder is made initially to carry
+part of the dead load, by adjustment, it will at once be
+recognised as a more complex matter. The measure of
+relief by which the old girderwork shall benefit need not
+be affected by the method of applying the centre girder,
+and may be decided on the principles already considered.
+The outer girders carrying a reduced load, when the bridge
+is fully loaded, and the cross-girders being in part supported
+at their centres in the manner already described, will give a
+resulting depression <i>m</i> (see <a href="#Fig71">Fig. 71</a>) of the centre cross-girders,
+below the original dead-load position, of a similar
+amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre
+girder, which may be designed to carry the required percentage<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span>
+of the total bridge loads with the maximum stress
+and depth, as conditions, leaving the initial dead load and
+necessary adjustments to be ascertained. This is the common
+case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.</p>
+
+<p>The centre girder of fixed depth being then required to
+carry a definite load at a definite flange stress, will deflect a
+definite amount at this stress. If this deflection equalled
+the extreme depression <i>m</i> of the old girder work, no adjustment
+would be necessary, the centre girder then carrying no
+initial dead load, as by the first method; but for centre
+girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally
+being small, and in order to ensure that the new girder shall
+do its full work, some dead load must be put upon it. In the
+act of adjustment the cross-girders must be lifted and the
+centre girder depressed, till the joint movement equals the
+excess <i>s</i> of the centre girder deflection over <i>m</i>, when the
+new girder will carry the proper amount of initial load, and
+upon further deflection under live load give the full measure
+of relief. The amount of &#8220;lift&#8221; or upward flexure of the
+old girder work, and the depression or &#8220;drop&#8221; of the new
+girder, during adjustment, will depend upon relative stiffness,
+and may be ascertained as follows<span class="nowrap">:&mdash;</span></p>
+
+<p>For unit reactions at the centre of the cross-girders the
+upward flexure of these may be ascertained, as also the
+upward flexure of the two outer girders when subject to
+forces of the same total amount (one-half to each) applied
+at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are
+subject to unit lifting forces; similarly, the depression of
+the centre girder for unit loads applied at the cross-girders
+may be determined. There will then be known the movements<span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span>
+upwards and downwards of the old and new work
+when being drawn together by unit forces applied as stated.</p>
+
+<p>If</p>
+
+<table class="formula nowrap" summary="Table page 128">
+
+<tr>
+<td class="left"><i>l</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">lift due to unit loads,</td>
+</tr>
+
+<tr>
+<td class="left"><i>l<sub class="lg">t</sub></i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">total lift due to adjustment,</td>
+</tr>
+
+<tr>
+<td class="left"><i>d</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">drop due to unit loads,</td>
+</tr>
+
+<tr>
+<td class="left"><i>d<sub class="lg">t</sub></i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">total drop due to adjustment,</td>
+</tr>
+
+<tr>
+<td class="left"><i>s</i></td>
+<td class="center padl1 padr1">=</td>
+<td class="left">deflection excess = gross adjustment,</td>
+</tr>
+
+</table>
+
+<p>there will then be</p>
+
+<p class="formula"><span class="division"><span class="num"><i>d</i></span>
+<span class="denom"><i>l</i> + <i>d</i></span></span> &times; <i>s</i> = <i>d</i><sub class="lg"><i>t</i></sub>,</p>
+
+<p>total drop of centre girder under adjustment,</p>
+
+<p class="formula"><span class="division"><span class="num"><i>l</i></span>
+<span class="denom"><i>l</i> + <i>d</i></span></span> &times; <i>s</i> = <i>l</i><sub class="lg"><i>t</i></sub>,</p>
+
+<p>total lift of centre cross girders under adjustment,</p>
+
+<p class="formula"><span class="division"><span class="num"><i>d</i><sub class="lg"><i>t</i></sub></span><span class="denom"><i>d</i></span></span> &times; unit load =</p>
+
+<p>initial load put upon centre girder at each cross-girder.</p>
+
+<p>The rise of the two outer girders for upward forces
+together equal to those depressing the centre girder may
+readily be deduced.</p>
+
+<div class="figcenter"><a name="Fig72" id="Fig72"></a>
+<img src="images/illo141.png" alt="" width="350" height="321" />
+<p class="caption"><span class="smcap">Fig.</span> 72.</p>
+</div>
+
+<div class="figcenter"><a name="Fig73" id="Fig73"></a>
+<img src="images/illo142.png" alt="" width="500" height="258" />
+<p class="caption"><span class="smcap">Fig.</span> 73.</p>
+</div>
+
+<p>The act of adjustment may conveniently be effected by
+the arrangement shown in <a href="#Fig72">Fig. 72</a>, in which each cross-girder
+is hung up at its centre by four bolts. At the middle of
+the centre girder the total amount to be screwed up will be
+that corresponding to the deflection excess <i>s</i>, but towards
+the ends this amount decreases, and may advantageously be
+represented by a diagram as <a href="#Fig73">Fig. 73</a>, in which, if <i>s</i> represents
+to scale the amount to be screwed up at a centre cross-girder,
+the corresponding amounts for other girders may be read off
+direct. It will be apparent that it must be necessary to<span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span>
+place the centre girder at such a height as to leave a space
+between the old and the new work greater than the amount
+to be screwed up, this excess clearance being ultimately filled
+by a packing.</p>
+
+<p>The precautions to be observed in carrying out this
+kind of work, and the practical methods of adjustment
+adopted by the author after some little experience, may here
+be given.</p>
+
+<p>Great care is necessary at the outset to ascertain the true
+spacing of the cross-girders, to ensure that the bolt-holes in
+the bottom flange of the centre girder shall come where
+desired. The fixing of the cross-girder brackets also needs
+close attention to avoid after trouble, the bolt-holes in the
+brackets being preferably drilled on the site after fixing.
+It will, for masonry abutments, be necessary to fix bedstones
+to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span>
+leave the stones liable to settle slightly when the full load
+is carried. To eliminate the bad effect of this upon the
+ultimate adjustment, and to take up any initial set of the
+new girder work, which would be prejudicial in the same
+way, it is desirable, the centre girder being in place, to screw
+up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it
+is convenient to prepare, for use at the bridge, a diagram
+somewhat similar to <a href="#Fig73">Fig. 73</a>, giving the amount by which
+the new and old work are to be brought together at each
+cross-girder, with the number of turns for each nut to effect
+this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is
+repeated as often as necessary, and so managed as to bring
+all up proportionately to the final requirement, keeping tally
+with chalk marks over each cross-girder as a check. The
+preliminary screwing up should be conducted with little less
+care than that adopted for the later adjustment, to avoid
+damage to the old work. This later adjustment having in
+due course been effected, it is then necessary to measure for
+packings to fill the spaces remaining between the old cross-girders<span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span>
+and the new centre girder. These spaces should be
+callipered at each of the four corners, care being taken to
+avoid after-confusion. The measurements ascertained will,
+however, be too great for the finished packings, as an allowance
+of not less than <sup>1</sup>&#8260;<sub>10</sub> inch (total), will commonly be
+wanted to cover irregularities in the surfaces. The packings,
+having been prepared and checked, may be slipped into
+place after slacking all the bolts a small amount to permit
+this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last
+operation.</p>
+
+<p>As a check upon the calculations and adjustment, the
+&#8220;lift&#8221; of the outer girders and cross-girders, and the &#8220;drop&#8221;
+of the centre girder may be observed by levelling. For this
+purpose the author has used a staff of inches divided into
+tenths, with which, and a good level, very accurate readings
+may be taken for short distances.</p>
+
+<p>No reference has been made to the effect of skew in a
+bridge on the above methods, the explanation given applying
+rather to bridges square on plan. The influence of skew on
+the load distribution will largely be a matter of detailed
+calculation. The flexure of the girders may also be sensibly
+affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to
+modify the amount of screwing up during adjustment, which
+may be better understood by reference to <a href="#Fig74">Fig. 74</a>, and comparing
+it with <a href="#Fig73">Fig. 73</a>, the adjustment diagram for a square
+bridge.</p>
+
+<p>To illustrate how these methods of strengthening work
+out, and compare as to weights of centre girders required,
+the case has been assumed of a wrought iron bridge of 60-feet
+span, having outer girders 5 feet deep, of 39 square inches
+gross flange area; and cross-girders, at 8-feet centres, 27-feet
+span, 1 foot 9 inches deep, with a gross flange area of twenty<span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span>
+square inches. The dead load and live load on either road
+are each 1&middot;75 tons per foot run.</p>
+
+<p>The stress in the outer girders previous to the alteration
+being 6 tons per square inch gross, it is desired to relieve
+this to the extent of 33 per cent. by a steel centre girder.
+In the table here given the quantities given in italics are
+fixed as primary conditions<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Centre Strengthening Girders for 60-ft. Span.</span></p>
+
+<table class="nowrap" summary="Table page 132">
+
+<tr class="bt bb">
+<th class="center br">&mdash;</th>
+<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Stress<br />Unknown.</th>
+<th colspan="2" class="center padl1 padr1 br">Centre<br />Girder,<br />Depth<br />Unknown.</th>
+<th colspan="2" class="center padl1 padr1">Adjust-<br />ments<br />Unknown.</th>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Outer Girder.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Deflection under modified live load</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;42</td>
+<td class="center bot padl0 padr1">in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Lift of adjustment</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;153</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Cross Girders.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depression under live load&mdash;modified conditions of support</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1 br">in.</td>
+<td class="left bot padl3 padr0">&middot;13</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Extreme depression (<i>m</i>)</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1 br">&#8222;</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1 br">&#8222;</td>
+<td class="left bot padl3 padr0">&middot;55</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Lift of adjustment (cross-girder only)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;095</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Total lift of adjustment (<i>l<sub class="lg">t</sub></i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;248</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="center padl1 padr1 br highline"><i>Centre Girder.</i></td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="br highline">&nbsp;</td>
+<td colspan="2" class="highline">&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depth</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>3&middot;5 ft.</i></td>
+<td colspan="2" class="center bot padl1 padr1 br">8&middot;2 ft.</td>
+<td colspan="2" class="center bot padl1 padr1"><i>3&middot;5 ft.</i></td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Unit stress on gross section (ex girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">2&middot;14 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>5&middot;0 tons</i></td>
+<td colspan="2" class="center bot padl1 padr1"><i>5&middot;0 tons</i></td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Total deflection (ex girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">&middot;55 in.</td>
+<td colspan="2" class="center bot padl1 padr1 br">&middot;55 in.</td>
+<td class="left bot padl2 padr0">1&middot;28</td>
+<td class="center bot padl0 padr1">in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Deflection excess (<i>s</i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;73</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Depression, or &#8220;drop&#8221; of adjustment (<i>d<sub class="lg">t</sub></i>)</td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td colspan="2" class="center bot padl1 padr1 br"><i>nil</i></td>
+<td class="left bot padl3 padr0">&middot;482</td>
+<td class="center bot padl0 padr1">&#8222;</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Gross area of flange</td>
+<td colspan="2" class="center bot padl1 padr1 br">105 sq. in.</td>
+<td colspan="2" class="center bot padl1 padr1 br">19&middot;2 sq. in.</td>
+<td colspan="2" class="center bot padl1 padr1">44&middot;5 sq. in.</td>
+</tr>
+
+<tr>
+<td class="left top padl1 padr1 br wrappable">Weight</td>
+<td colspan="2" class="center bot padl1 padr1 br">20 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br">10&middot;4 tons</td>
+<td colspan="2" class="center bot padl1 padr1">11&middot;4 tons</td>
+</tr>
+
+<tr class="bb">
+<td class="left top padl1 padr1 br wrappable">Net flange stress (including girder&#8217;s weight)</td>
+<td colspan="2" class="center bot padl1 padr1 br">3&middot;19 tons</td>
+<td colspan="2" class="center bot padl1 padr1 br">6&middot;87 tons</td>
+<td colspan="2" class="center bot padl1 padr1">6&middot;94 tons</td>
+</tr>
+
+</table>
+
+<p>Girders subject to distributed load are treated as having<span class="pagenum"><a name="Page_133" id="Page_133">[133]</a></span>
+uniform stress, but where this is not strictly the case, as in
+some light girders, it will be necessary to take the fact into
+account. For centre girders of wrought iron, and a unit
+stress on the gross section of 4 instead of 5 tons, the girder
+weights are between 9 and 10 per cent. greater.</p>
+
+<div class="figcenter"><a name="Fig74" id="Fig74"></a>
+<img src="images/illo145.png" alt="" width="500" height="237" />
+<p class="caption"><span class="smcap">Fig.</span> 74.</p>
+</div>
+
+<p>In the above treatment of the application of centre
+strengthening girders there is a source of error which should
+be touched upon. If, under live load, the centre girder
+deflects more than the outer girders, as it commonly will,
+there must be a want of uniformity in the behaviour of the
+cross-girders, those near the abutments being more relieved
+than the estimated amount of relief of those at the centre,
+which will have less than that intended; but the reduction
+of stress in the cross-girders will generally be so considerable
+that any such ambiguity of excess or defect is commonly
+unimportant; the effect of this also upon the main girders
+is much less than might be supposed, being, for the third of
+the cases just given, about 2<sup>1</sup>&#8260;<sub>2</sub> per cent. excess for the centre
+girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as
+approximate only. It is possible to eliminate some part of<span class="pagenum"><a name="Page_134" id="Page_134">[134]</a></span>
+the error by lifting the end cross-girders during adjustment,
+a less amount than that given by the diagrams, <a href="#Fig73">Figs. 73</a> and
+<a href="#Fig74">74</a>, taking care that the centre girder is depressed its full
+amount by lifting the centre cross-girders a little more; this
+refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.</p>
+
+<p>Particulars are here given of five ordinary cases, comparing
+the calculated and observed results of adjustment. The
+operation of levelling was conducted by a quick-eyed and
+capable assistant, who was not made acquainted with the
+results expected, in order to avoid any sub-conscious tendency
+to match the calculated figures<span class="nowrap">:&mdash;</span></p>
+
+<p class="center"><span class="smcap">Examples of Centre Girder Adjustments.</span></p>
+
+<table class="nowrap" summary="Table page 134-135">
+
+<tr class="bt bb">
+<th class="center br">&mdash;</th>
+<th colspan="2" class="center padl1 padr1 br">Calculated.</th>
+<th colspan="2" class="center padl1 padr1">Observed.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th colspan="2" class="center padl1 padr1 br">in.</th>
+<th colspan="2" class="center padl1 padr1">in.</th>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 1.&mdash;56-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;82</td>
+<td colspan="2" class="center padl1 padr1">&middot;84</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;23</td>
+<td colspan="2" class="center padl1 padr1">&middot;22</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;20</td>
+<td colspan="2" class="center padl1 padr1">&middot;10 and &middot;13</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 2.&mdash;57-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;50</td>
+<td colspan="2" class="center padl1 padr1">&middot;50</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;18</td>
+<td colspan="2" class="center padl1 padr1">&middot;20</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;11</td>
+<td colspan="2" class="center padl1 padr1">&middot;08 and &middot;10</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 3.&mdash;67-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;70</td>
+<td colspan="2" class="center padl1 padr1">&middot;75</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;15</td>
+<td colspan="2" class="center padl1 padr1">&middot;17</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;10</td>
+<td colspan="2" class="center padl1 padr1">&middot;09</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 4.&mdash;68-<i>Ft. Span.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;70</td>
+<td colspan="2" class="center padl1 padr1">&middot;65</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders at centre</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;20</td>
+<td colspan="2" class="center padl1 padr1">&middot;18</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td colspan="2" class="center padl1 padr1 br">&middot;13</td>
+<td colspan="2" class="center padl1 padr1">&middot;14</td>
+</tr>
+
+<tr>
+<td colspan="5" class="center highline">No. 5.&mdash;52-<i>Ft. and</i> 28-<i>Ft. Spans continuous.<span class="pagenum"><a name="Page_135" id="Page_135">[135]</a></span></i></td>
+</tr>
+
+<tr class="bb">
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1 br">Long<br />Span.</th>
+<th class="center padl1 padr1 br">Short<br />Span.</th>
+<th class="center padl1 padr1 br">Long<br />Span.</th>
+<th class="center padl1 padr1">Short<br />Span.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1">in.</th>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Depression of centre girder</td>
+<td class="center padl1 padr1 br">&middot;28</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;29</td>
+<td class="center padl1 padr1">..</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of centre girder</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;04</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1">&middot;03</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of cross-girders (centre of spans)</td>
+<td class="center padl1 padr1 br">&middot;17</td>
+<td class="center padl1 padr1 br">&middot;09</td>
+<td class="center padl1 padr1 br">&middot;15</td>
+<td class="center padl1 padr1">&middot;13</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">Lift of outer girders</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;08</td>
+<td class="center padl1 padr1">..</td>
+</tr>
+
+<tr class="bb">
+<td class="left padl1 padr1 br">Depression of outer girder</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1 br">&middot;01</td>
+<td class="center padl1 padr1 br">..</td>
+<td class="center padl1 padr1">negli-<br />gible.</td>
+</tr>
+
+</table>
+
+<p>The method of calculation adopted for these cases was
+not precisely that given, though depending upon the same
+broad principles. The first cannot be considered a good
+example. The last, having continuous girders, of course
+needed special treatment.</p>
+
+<p>Of about seventeen bridges strengthened in the manner
+described, the effect generally was satisfactory, in reducing
+deflection and vibration; but in two cases of small span,
+owing probably to settlement of bedstones, the results were
+not so good.</p>
+
+<p>From first to last the work of putting in a centre girder
+takes some little time, owing to the slow progress generally
+made in fixing the brackets, preparing packings, etc. The
+cost of a typical case was about 23 per cent. of the cost of a
+new superstructure, with a 30 per cent. relief of stress.</p>
+
+<div class="figcenter"><a name="Fig75" id="Fig75"></a>
+<img src="images/illo148.png" alt="" width="500" height="303" />
+<p class="caption"><span class="smcap">Fig.</span> 75.</p>
+</div>
+
+<div class="figcenter"><a name="Fig76" id="Fig76"></a>
+<img src="images/illo149.png" alt="" width="500" height="283" />
+<p class="caption"><span class="smcap">Fig.</span> 76.</p>
+</div>
+
+<p>A special case of strengthening by a centre girder, having
+considerable interest, may be here referred to. The primary
+idea involved was not the author&#8217;s. The bridge dealt with
+has already been noticed under &#8220;<a href="#Page_34">Bracing</a>&#8221; and a section,
+before alteration, shown in <a href="#Fig26">Fig. 26</a>. The span being 85
+feet, there was no room for a centre girder of sufficient depth
+above the cross-girders and between the roads, nor was it
+considered economical to place the girder wholly below the<span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span>
+floor, because of the costly staging this would have necessitated
+for erection purposes, the height above ground level
+being very great. A girder was therefore designed, having
+open latticing at an angle of 60 degrees, with a bottom boom
+to be below the cross-girders, the top being as high above
+the rails as could be permitted (see <a href="#Fig75">Figs. 75</a> and <a href="#Fig76">76</a>). A
+temporary boom was arranged at the intersection of diagonals,
+the lower boom proper not being fixed till the girder
+having been lifted into place, with the diagonal members
+passing between the cross-girders, allowed this to be done.
+The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being
+then 2 inches. The permanent boom was then put in place,
+and the girder restored as nearly as was practicable to the
+camber it was intended to have when complete, but without
+throwing, during the process, any improper loads upon the
+old work.</p>
+
+<p>The lower boom being finally riveted up, the cross-girders
+were made to bear upon it by suitable packings. There
+were, in addition to the new girder, two stiff frames between
+the old main girders, to which the new was secured.</p>
+
+<p><span class="pagenum"><a name="Page_137" id="Page_137">[137]</a></span></p>
+
+<p>The girder was designed with the intention that under
+dead load only the cross-girders should just rest, but throw
+no weight, upon the new work, the latter assisting to carry
+live load only. The floor beams being of small span, and
+securely riveted to the old girder tops, the centre girder was
+required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion,
+the three points of support of the cross-girders thus not
+altering their relative levels. That this resulted was evident
+from the fact that, previous to connecting the cross-frames
+to the centre-girder, the work being otherwise complete, a
+space between the two of about <sup>1</sup>&#8260;<sub>2</sub> inch, afterwards filled by
+a packing, showed no alteration, the closest measurement
+failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be
+expected, very marked.</p>
+
+<p>In the conduct of that class of strengthening work which
+has been dealt with in this chapter, it is essential, in the
+author&#8217;s judgment, that the man responsible for the detailed
+calculations and design should himself see the operations of<span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span>
+adjustment carried out, or delegate it only to one equally
+familiar with the requirements.</p>
+
+<p>Before dismissing the subject, it will be well to refer to
+a method of approximately determining flexure curves, of
+occasional use in dealing with centre girder or similar questions.
+The figure assumed is plotted to an exaggerated scale,
+with which object the actual radius of curvature at points
+along the girder&#8217;s length are first ascertained by the formula</p>
+
+<p class="formula"><span class="division"><span class="num">E &times; D</span><span class="denom"><i>f</i> &times; 2</span></span> = R, radius of curvature in feet,<br />
+</p>
+
+<p>and the radius of curvature for the diagram by</p>
+
+<p class="numform"><a name="Form5" id="Form5"></a><span class="formula">12 &times; R &times; F<sup>2</sup> = <i>r</i>, radius for plotting, in inches</span>
+<span class="number">(5)</span></p>
+
+<p>E being the modulus of elasticity, D the girder&#8217;s depth in
+feet, <i>f</i> the mean of the extreme flange stresses per square
+inch of gross area, and F the fraction indicating scale as <sup>1</sup>&#8260;<sub>48</sub>,
+where <sup>1</sup>&#8260;<sub>4</sub> inch = 1 foot. The curve, being plotted, shows by
+direct scaling the movement of any point relative to its
+original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn
+with the help of template curves, or even set out as pieces of
+&#8220;straight.&#8221;</p>
+
+<p>When the curve is laid down so that its chord equals the
+span to scale, the method involves an error of excess in the
+resulting deflection or droop which is as much as 7 per cent.
+when the mean radius for plotting equals the span as drawn,
+or when the droop of curve approaches one-eighth of the
+span. As the exaggeration of curvature is made less pronounced,
+this error rapidly diminishes, till for a droop of
+about one-sixteenth the percentage is one-fourth part of that
+above given. This excess in the droop of curve may be
+amended by the following expression<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula">droop - <span class="fsize150">(</span><span class="division"><span class="num">droop<sup>3</sup></span><span class="denom">chord<sup>2</sup></span></span>
+&times; 3&middot;73<span class="fsize150">)</span> = corrected droop, or deflection.</p>
+
+<p><span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span></p>
+
+<p>For some purposes it may be preferable to amend the
+radii for plotting, so that the curve, as laid down, shall be<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span>
+correct, which may be effected by the formula here given, to
+be applied to each value of r, as first ascertained<span class="nowrap">:&mdash;</span></p>
+
+<p class="formula"><i>r</i> + <span class="fsize150">(</span><span class="division"><span class="num">chord<sup>2</sup></span>
+<span class="denom"><i>r</i></span></span> &times; &middot;0625<span class="fsize150">)</span> = corrected plotting radius.</p>
+
+<p>If, however, the length of curve is made equal to the
+span (the chord then being less), and the radii for plotting
+as given by <a href="#Form5">(5)</a> are used, the result will for most purposes
+be sufficiently precise, though there will now be an error of
+a contrary kind, which, for a curve having a droop of one-eighth,
+will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described
+by Professor Fleeming Jenkin in the article &#8220;Bridges&#8221; of
+the &#8220;Encyclop&aelig;dia Britannica,&#8221; but without corrections.</p>
+
+<p>A careful comparison of results by the above means, with
+those calculated, shows that with good draughtsmanship they
+may be relied upon for considerable accuracy. Equally
+applicable to girders of varying depth and flange stress,
+they have also a limited use in cases of continuity.</p>
+
+<div class="figcenter"><a name="Fig77" id="Fig77"></a><a name="Fig78" id="Fig78"></a>
+<img src="images/illo151.png" alt="" width="264" height="550" />
+<p class="caption"><span class="smcap">Figs.</span> 77 and 78.</p>
+</div>
+
+<p><a href="#Fig77">Figs. 77 and 78</a> illustrate the deflection and stress diagrams
+for the cross-girders of the bridge supposed to have
+been strengthened by a centre-girder, when under the
+influence of live load and a centre reaction of a definite
+amount. As a matter of convenience, each radius length
+has been halved, before correction, so that the resulting
+droop of the curve is twice the true amount.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span></p>
+
+<h2>CHAPTER XII.<br />
+<span class="chaptitle">CAST-IRON BRIDGES.</span></h2>
+
+<p>Cast Iron as a material for bridges has of late years fallen
+into disrepute. It is now entirely tabooed by the Board of
+Trade for railway under-bridges, unless of arched construction.
+This condemnation of cast iron followed, and was
+apparently the result of, an accident which occurred to an
+under-bridge on one of the southern lines, which bridge had
+already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good,
+inasmuch as it led to a thorough overhaul of all railway
+under-bridges in this country, and the renewal of a great
+number no longer in a condition suited to the carriage of
+heavy or of passenger traffic; yet there is little doubt
+that, in the author&#8217;s judgment, many excellent cast-iron
+bridges were then removed at considerable cost, to be replaced
+by others of wrought iron or steel, which will not last
+so long as many of those displaced had done, or would still
+have lasted had they not been dismantled.</p>
+
+<p>The earlier cast-iron bridges were commonly made of
+cold-blast iron, a material of such strength and toughness as
+to give an extraordinary amount of trouble in breaking up
+the heavier parts, when the time arrived to do this, and with
+which material ordinary hot-blast iron is not to be compared
+for reliability.</p>
+
+<div class="figcenter"><a name="Fig79" id="Fig79"></a>
+<img src="images/illo154.png" alt="" width="500" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 79.</p>
+</div>
+
+<p>As illustrating the very considerable stress to which cast
+iron may be subjected, without of necessity leading to any
+mishap, two cases may be cited. The first, a bridge of 32<span class="pagenum"><a name="Page_142" id="Page_142">[142]</a></span>
+feet effective span, carrying two lines of way, each pair of
+rails being supported upon Barlow rails, forming the bridge
+floor, the ends resting upon the bottom flanges of inverted
+<span class="lettsymb">T</span>-shaped girders, 2 feet 3 inches deep, as shown in <a href="#Fig79">Fig. 79</a>.</p>
+
+<p>The extreme fibre stress works out at 2&middot;9 tons per square
+inch in tension, and 5&middot;9 tons per square inch compression,
+calculated as it would be in ordinary office work; but for
+the actual loads, at a span as above, exceeding the clear span
+by 6 inches only, and without regard to the effects of eccentric
+application of the load. The girders when taken out showed
+upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be
+too strongly condemned, notwithstanding that in this case no
+ill resulted. It is evident that a piece of the lower flange
+being broken out from this cause, as occasionally happens,
+might so reduce the section as to result in complete failure.</p>
+
+<div class="figcenter"><a name="Fig80" id="Fig80"></a><a name="Fig81" id="Fig81"></a>
+<img src="images/illo155.png" alt="" width="500" height="382" />
+<p class="caption"><span class="smcap">Figs.</span> 80 and 81.</p>
+</div>
+
+<p>The second example is that of a small railway under-bridge
+of two spans, continuous over the central pier, each
+span being 16 feet 6 inches. The rails were supported upon
+longitudinal timbers lying within trough-shaped girders, as
+shown in <a href="#Fig80">Figs 80 and 81</a>.</p>
+
+<p>The stress over the pier, in the extreme fibres of the top
+flange, is estimated at 4&middot;7 tons per square inch in tension,
+but it should be noted that the effect of the timber longitudinal
+and rail has been neglected in arriving at this result,<span class="pagenum"><a name="Page_143" id="Page_143">[143]</a></span>
+which might possibly on this account be reduced to near
+3 tons per square inch.</p>
+
+<p>The case is noticeable because no evidence of high stress
+was apparent. The author saw nothing to suggest sinking
+of the central pier, the effect of which, within limits, would
+be to further reduce the stress as calculated; but it is quite
+possible some slight settlement had occurred; this, as the
+spans were so small, would have a sensible effect. While too
+much reliance should not, it is clear, be placed upon any
+estimated result about which there is a lingering doubt, it
+should be remarked that, as it would be necessary the pier
+should sink <sup>3</sup>&#8260;<sub>16</sub> of an inch, for each ton of reduced stress, it
+is not probable that the results quoted are in excess to any
+material degree; they are, indeed, more probably low, as no
+notice has been taken of impact.</p>
+
+<p>Though cast-iron girders for railway under-bridges are
+now prohibited in this country for new works, there are still
+uses to which they may be applied, and it may be well to
+insist that girders of this material should be fairly loaded, the<span class="pagenum"><a name="Page_144" id="Page_144">[144]</a></span>
+weight being brought upon them in such a way that there
+shall be no serious secondary stress, such as arises when wide
+flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking
+down under a load fairly applied. Preference is now given
+to steel or wrought iron for columns; while this is often
+quite justifiable, there remain many cases in which nothing
+better need be desired for this purpose than good cast iron,
+provided only that the column be loaded in a suitable
+manner&mdash;i.e., axially, and that the arrangement and details
+of the super-structure are such that there shall be no cross-breaking
+efforts, or rocking of the column due to temperature
+or other causes; unless, indeed, such cross-breaking or
+rocking is definitely taken into account in designing the work.
+The same care observed in the detailing of cast-iron work
+that is not infrequently taken in the design of structures
+made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with
+the advantage of greater resistance to rust, and a reduced
+cost in maintenance.</p>
+
+<p>Good cast iron is, in fact, when used with discretion, a
+most excellent material, popular predjudice notwithstanding.
+The oldest metallic bridge in this country at the present
+moment is of that metal.</p>
+
+<p>The one chief respect in which cast iron is at a disadvantage
+compared with wrought iron or steel is that it does not
+give premonitory warning of failure&mdash;it remains intact, or it
+breaks. The indications of weakness, which may be read by
+an experienced inspector of other metallic bridges, are in
+a great measure absent. There is also an objection which
+may exist, but is to be avoided by good design and care in
+the foundry&mdash;viz., internal stress due to unequal cooling.
+In extreme cases this may lead to fracture before the work<span class="pagenum"><a name="Page_145" id="Page_145">[145]</a></span>
+has left the maker&#8217;s hands, but it can only occur by neglect
+of ordinary precautions.</p>
+
+<div class="figcenter"><a name="Fig82" id="Fig82"></a><a name="Fig83" id="Fig83"></a>
+<img src="images/illo158a.png" alt="" width="550" height="265" />
+<p class="caption"><span class="smcap">Figs.</span> 82 and 83.</p>
+</div>
+
+<p>In a case which has already been referred to in the
+chapter on &#8220;<a href="#Page_73">Deformations</a>,&#8221; <a href="#Page_80">page 80</a>, an outer rib of a
+cast-iron arch fractured near the crown after fifty-four years&#8217;
+use. Owing to the nature of the design, and the fact that
+the near abutment had closed in slightly, bringing the linear
+arch of necessity near the lower edges of the arch segment
+in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces,
+at the upper edge where fracture commenced. The result
+was very far from explaining the occurrence of the break,
+but an examination of the details shown in <a href="#Fig82">Figs. 82 and 83</a>
+will make it apparent that, in addition to the tensile stress, as
+calculated, there was probably a severe initial stress of the
+same character due to irregular cooling in the foundry half a
+century before. The sum of these stresses, it is suggested,
+placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent
+either by producing a small further settlement of the foundations,
+of which the author saw no evidence, or, as is more
+probable, the attachment of a rope to this rib for the purpose
+of keeping a barge in position, which certainly did occur,
+gave the arch rib just such an additional strain as to result
+in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The
+inner ribs were of a much less objectionable section.</p>
+
+<div class="figcenter"><a name="Fig84" id="Fig84"></a>
+<img src="images/illo158b.png" alt="" width="550" height="182" />
+<p class="caption"><span class="smcap">Fig.</span> 84.</p>
+</div>
+
+<p>Cast-iron arches, though still allowed by the Board of
+Trade rules, are, indeed, liable to be seriously affected by
+settlement, or yielding of the abutments, unless hinges at the
+crown are introduced. As an instance of this may be quoted
+a bridge of some 45 feet span, in which the arches were cast
+in two pieces abutting, and very efficiently bolted together at
+the crown, the springing and vertical abutment member of<span class="pagenum"><a name="Page_146" id="Page_146">[146]</a></span>
+the spandrel being bolted and built solidly into heavy
+masonry. The arch sank at the crown, caused by, or itself
+the cause of, a movement of the abutment, with the result
+that the lower bolts at the crown joint broke away, rupturing
+the casting, as shown in <a href="#Fig84">Fig. 84</a>. The arch must then have
+acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if
+a proper hinge had originally been provided. The break
+happened to occur so as to leave a sufficiently good bearing<span class="pagenum"><a name="Page_147" id="Page_147">[147]</a></span>
+face at the crown; there was, indeed, no tendency for one
+surface to slide upon another; but in the accidental fracture
+of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.</p>
+
+<p>A second case of very much the same character has also
+been under the author&#8217;s observation, though in this the ends
+of the spandrels were not built into the brickwork of which
+the abutments were composed. Other instances of fracture
+either in the arch proper or in the spandrel work, have come
+under notice, though particulars cannot now be adduced;
+but the examples cited are by themselves sufficient to justify
+the conclusion that it is imprudent to construct a cast-iron
+arch without a central pin or its equivalent, unless the abutments,
+being exceptionally well founded, may be relied upon
+as free from any liability to move. It is, however, to be
+borne in mind that movement in the abutments of a small
+arch of any given absolute amount is more injurious than the
+same amount of movement in the abutments of large arches
+of similar design, so that what may be negligible in the latter
+case would perhaps be destructive in the former.</p>
+
+<p>To the absence of ductility and liability to initial stress
+must be added yet another disadvantage to which cast-iron
+work is prone&mdash;viz., the possibility of concealed defects,
+blow-holes or cold-shuts; these in good foundry practice are
+not very likely to occur, but, as they are possible, cannot
+be overlooked in considering the suitability of cast iron for
+bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks
+by way of qualification, the author reiterates his opinion that
+there is still a use for cast iron in bridgework.</p>
+
+<p>With respect to the repair of cast-iron bridges, but little
+is to be said; the possibilities in this direction are very
+limited. Occasionally it may be desired to deal with the
+fracture of some member in the spandrel bracing of an arch,<span class="pagenum"><a name="Page_148" id="Page_148">[148]</a></span>
+when it is commonly sufficient, and even preferable, to limit
+the repair work to confining the fractured parts in such a
+way as to prevent displacement.</p>
+
+<p>Rarely it may happen that an arch fractures as a result
+of settlement, or other movement, when, if it is decided that
+safety of the structure is not imperilled, it will in this case
+also be preferable to confine the parts simply by flitch-plates
+or other contrivance, with no attempt rigidly to make good
+the break, the consequences of which treatment would
+probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable,
+though something may occasionally be done by the
+negative process of lightening the dead load, or by remodelling
+the permanent way. Arches may, however, be
+rendered much more reliable by the introduction of suitable
+bracing where this is either wanting or inefficient.</p>
+
+<p>In scheming such additions it is desirable to arrange for
+as little drilling of the old work as is possible; where this
+cannot be altogether avoided, the position of the holes should
+be carefully chosen with regard to the effect they may have
+upon the strength of the old work.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_149" id="Page_149">[149]</a></span></p>
+
+<h2>CHAPTER XIII.<br />
+<span class="chaptitle">TIMBER BRIDGES.</span></h2>
+
+<p>Timber bridges, though probably the most ancient in
+type, are yet the least durable in any particular instance.
+The perishable nature of the material when used for exposed
+construction renders it peculiarly liable to develop defects
+which quickly put a limit to the life of the structure. In
+addition to decay in the body of the main members&mdash;which
+may perhaps be long delayed, so that a simple beam bridge
+may last for many years&mdash;there is in more complex designs
+decay at connections and joints, which proves very detrimental
+to the integrity of the whole. Water running upon
+the surface of a member gravitates to its lower end, and, if
+there be a joint or other connection, settles there, to be productive
+of lasting mischief. From this cause, together with
+a very common deficiency of bearing surface relative to the
+forces to be met, the joints soon develop some movement;
+working of the structure commences under passing loads, its
+final destruction being then a question of time only. Each
+joint is, in fact, in timber bridge construction a source of
+serious weakness to a degree which has no parallel in well-designed
+metallic bridges.</p>
+
+<p>Wrought-iron straps to confine the ends of raking
+members, or for other uses, are liable to crush into the wood,
+and bolts are apt to enlarge the hole through which they
+pass. Wood keys, where these are introduced to prevent one
+timber from sliding upon another, are also prone to develop
+cracks in the main members, and fibre crippling from excess<span class="pagenum"><a name="Page_150" id="Page_150">[150]</a></span>
+of stress. All these defects are, however, in timber-work
+more easily defined than efficiently remedied, as it is barely
+practicable for any but the harder woods to ensure, for heavy
+loads, a sufficiency of bearing surfaces.</p>
+
+<p>The most readily detected evidence of deterioration in
+timber bridges is the sag of its bearing members, or trusses,
+for the simple reason that if there is no local trouble at the
+joints, there will probably be no appreciable drop at the
+centre of the span. The existence of such a depression
+may, however, be caused in rare instances by the spread
+of the supporting piers or abutments, particularly in
+the case of beams trussed by end diagonal rakers and
+having no tie.</p>
+
+<p>Bridges formed of deep trusses, with the road upon the
+top, are sometimes found to be wanting in lateral bracing,
+the result of which is that the main trusses go out of line,
+leaning considerably one way or the other, being checked
+only by such rigidity as the joints and floor-beam attachments
+may have, with possibly some assistance from the end connections
+of the span.</p>
+
+<p>The decay of piles where entering the ground or water
+is, of course, a fruitful source of trouble, as also is the sinking
+of piles, where these are insufficient in number, or have
+not been well driven in the first place.</p>
+
+<p>A vital difficulty with timber structures generally is the
+uncertainty that will commonly exist as to how far decay
+extends in those cases where it has started. Timber does
+not necessarily show upon its surface the evidences of internal
+rotting. Memel timber may, indeed, be sometimes found
+to have become thoroughly unreliable, yet showing no sign
+of this upon its painted surface. By sounding the wood
+with a hammer, or by probing, its condition may commonly
+be ascertained. In cases of doubt, an auger-hole will make
+it clear as to whether the interior be good or otherwise, as<span class="pagenum"><a name="Page_151" id="Page_151">[151]</a></span>
+to the particular parts tested; but only as to those parts,
+leaving it a matter of guesswork as to the remainder.</p>
+
+<div class="figcenter"><a name="Fig85" id="Fig85"></a>
+<img src="images/illo164a.png" alt="" width="550" height="186" />
+<p class="caption"><span class="smcap">Fig.</span> 85.</p>
+</div>
+
+<p>A railway bridge having many of the defects which have
+been indicated may be quoted as an example. This structure
+crossed a canal, supported upon piles, some of which were in
+water, others carrying land spans. The canal span consisted
+of four trusses, one under each rail, or nearly so, framed in
+the manner shown in <a href="#Fig85">Fig. 85</a>, precise details not, however,
+being now available. The trusses, apart from deflection
+under live load, sagged considerably&mdash;in one instance,
+4<sup>1</sup>&#8260;<sub>2</sub> inches; one inside truss was also leaning towards the
+centre line of the bridge as much as 3 inches. One raker,
+or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections
+and joints were also in a bad condition. The vertical
+tie-bolts of the main trusses were all slack. The piles
+generally, many of which were badly decayed, had sunk and
+inclined towards one end of the bridge about 4 inches in
+7 feet of height, the ground being soft and unreliable.</p>
+
+<p>Movement under a passenger train crawling over the
+bridge was very appreciable, but not startling. There had
+been introduced, from time to time, additional timbers and
+iron ties, with the object of rendering the spans more reliable,
+but leaving it somewhat difficult to determine the function
+of the several members. The bridge was, of course, reconstructed.</p>
+
+<div class="figcenter"><a name="Fig86" id="Fig86"></a>
+<img src="images/illo164b.png" alt="" width="550" height="182" />
+<p class="caption"><span class="smcap">Fig.</span> 86.</p>
+</div>
+
+<div class="figc550"><a name="Fig87" id="Fig87"></a><a name="Fig88" id="Fig88"></a>
+<img src="images/illo165.png" alt="" width="550" height="209" />
+<p class="caption_b"><span class="left49"><span class="smcap">Fig.</span> 87.</span> <span class="right49"><span class="smcap">Fig.</span> 88.</span></p>
+<p class="caption_e"><span class="smcap">Fig.</span> 87. and <span class="smcap">Fig.</span> 88.</p>
+</div>
+
+<p>An instance may here be cited showing how badly distorted
+a timber structure may become without actually
+falling. The bridge referred to consisted of three spans of
+29 feet, each span having two trusses, between which ran
+a colliery tramroad, 1-foot 6-inch gauge; the corves running
+upon this, at 4 feet 6 inch centres, weighed, when full,
+about 10 cwt. each. The trusses were badly out of shape,
+the centre span having sagged 5<sup>1</sup>&#8260;<sub>2</sub> inches, with one truss of<span class="pagenum"><a name="Page_152" id="Page_152">[152]</a></span>
+the same span nearly 10 inches out of line at the centre.
+This little bridge, of which some details are shown in <a href="#Fig86">Figs.
+86</a>, <a href="#Fig87">87, and 88</a>, had been in use about twenty years.</p>
+
+<div class="figcenter"><a name="Fig89" id="Fig89"></a>
+<img src="images/illo166.png" alt="" width="600" height="212" />
+<p class="caption"><span class="smcap">Fig.</span> 89.</p>
+</div>
+
+<p>A third case which may be named is that of a road bridge,
+about 12 feet wide, crossing by thirteen spans a shallow river
+liable to floods. The construction was of a simple character,
+as indicated in <a href="#Fig89">Fig. 89</a>, and consisted of piles supporting
+trussed beams, which had sagged in some instances over<span class="pagenum"><a name="Page_153" id="Page_153">[153]</a></span>
+2<sup>1</sup>&#8260;<sub>2</sub> inches. The bridge had, some years previous to the
+author&#8217;s inspection, been heavily repaired, many new strut
+and stretching pieces having been introduced, the piles also
+being reinforced or renewed. Five years before, a traction
+engine, said to weigh 5 tons, had passed across the bridge in
+safety; but the author noticed that a coal wagon, which,
+with the horse, weighed about 50 cwt., when walked slowly
+over set up much movement. This bridge had been in use
+nearly thirty years, and was very much out of line from end
+to end.</p>
+
+<p>Though timber bridges cannot at the best be considered
+durable, yet, by attention to certain points in design and
+construction, their length of life may be materially enhanced.<span class="pagenum"><a name="Page_154" id="Page_154">[154]</a></span>
+Every cut across the grain may be considered an element of
+weakness by exposing the material to quicker decay, for which
+reason the number of ends, or of joints, should be reduced
+to a minimum. An additional reason for reducing the
+number of joints or other
+connections is the liability
+of these to develop movement,
+as already stated, the
+yield of any one joint, being
+the cause of movement in
+others, which might, but for
+this, have remained close.
+These considerations lead
+to the conclusion that fewness
+of parts is, in timber
+construction, as in structural
+work generally, an excellent
+principle to observe. Mortising,
+elaborate scarf joints,
+recessing, or any cutting into
+the timber which is not essential,
+should be avoided, the
+simplest forms of connection
+being preferable, if at
+all suitable. If a step or
+butt surface is wanted for
+any member, it is commonly
+better to provide this by a
+cleat or other added piece,
+rather than by cutting into the timber butted against.</p>
+
+<p>A complicated joint formed in the body of main timbers
+can only be renewed by renewal of the timber itself, whereas
+by the method indicated the joint is readily tightened, or
+re-made, without involving the main member. Bearing<span class="pagenum"><a name="Page_155" id="Page_155">[155]</a></span>
+surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake
+of bearing surface in the holes, and reduction of any
+liability to bend under cross-stress. In trusses of the
+form shown in <a href="#Fig85">Figs. 85</a> and <a href="#Fig86">86</a>, it is desirable to introduce
+diagonal members in the middle bay, even though it
+may appear that the stiffness of the main beams is sufficient
+to render this unnecessary as a matter of strength, as without
+these there is apt to be, under rolling load, a slight
+distortion, leading to working of the joints and free entry
+of moisture. Lateral bracings should also, for much the
+same reasons, be introduced, even though they may not
+appear necessary in the new structure, with joints all close
+and effective.</p>
+
+<p>Projecting ends of timbers should be carried out well
+beyond the requirement of strength or bearing, in order to
+ensure a liberal margin for that decay in the end fibres which
+commonly develops. Timbers resting upon abutments, or
+running into confined spaces, should be arranged for free
+ventilation and ready drying. Occasionally joints at the
+lower ends of timbers are protected by lead or zinc flashings
+to prevent water running into them, a method which should
+have some protective value. Whatever measures may be
+adopted, whether in the design or execution of timber bridge-work,
+will, however, be but little effective, if the timber itself
+is not good of its kind, and well seasoned.</p>
+
+<p>Creosoting to be useful should be thorough and something
+more than skin deep. The timber itself should be well dried
+before treatment.</p>
+
+<p>The repair of timber bridges very largely consists in the
+renewal of decaying timbers, where this is practicable, or in
+adding supplementary pieces where the old cannot conveniently
+be displaced. Joints may be tightened up by
+hard-wood wedges, properly secured to prevent slacking back,<span class="pagenum"><a name="Page_156" id="Page_156">[156]</a></span>
+all bolts being also screwed up tight, perhaps some additional
+being introduced.</p>
+
+<p>Piles standing in water, which have decayed, may be
+strengthened by driving other piles between the old, or on
+either side, but not of necessity opposite to them, and by
+means of waling timbers bolted to the old piles, put in a
+position to take load, either by the walings resting upon
+their tops, or being bolted to them. Piles decayed where
+entering solid ground may generally be strengthened by
+bolting on supplementary timbers to reach well above and
+below the decayed part, or by cutting out the bad length,
+introducing a new piece, and fishing the butt-joints in a
+proper manner. But all remedial measures have generally
+to be considered with reference to cost, as compared with
+the probable increase of life of the structure. With a bridge
+in an advanced state of decrepitude, such repairs may prove
+anything but economical, and at the best defer reconstruction
+but a very moderate length of time.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_157" id="Page_157">[157]</a></span></p>
+
+<h2>CHAPTER XIV.<br />
+<span class="chaptitle">MASONRY BRIDGES.</span></h2>
+
+<p>Masonry bridges, in which description it is intended to
+include structures both in stone and brick, are, when well
+built, amongst the most durable and long-suffering of any
+which come under the care of a maintenance engineer; yet
+when developing the faults peculiar to their kind, they may
+be the occasion of much anxiety, and render necessary frequent
+inspection, or even continuous watching.</p>
+
+<p>Apart from decay of mortar or material, defects may very
+commonly be traced to the foundations, or to earth-slips.
+Sinking, when uniform, may be quite harmless, though
+possibly inconvenient; irregular sinking of piers or abutments
+is quite a different matter. It is, however, remarkable
+to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and
+kind which would be fatal to the connections of metallic
+bridgework is endured by bridges of stone or brick; not, it
+may be, without damage, yet with no occasion for alarm.
+The superstructure of metallic bridges may often, however,
+be restored to the true level before the mischief has become
+serious, whereas in the case of masonry arches this is not
+practicable.</p>
+
+<p>Spreading of the abutments is very seldom the cause of
+any great injury to an arch, though it is common enough to
+find old and flat arches slightly down at the crown; but the
+contrary case of abutments closing in is not very unusual
+when these are high, or terminate a viaduct over a deep<span class="pagenum"><a name="Page_158" id="Page_158">[158]</a></span>
+valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected;
+or, if the arches are very solid and heavy, the abutment may
+slide forward at the base, with no sensible reduction of the
+opening.</p>
+
+<p>When a viaduct connects the two ends of a high embankment,
+it may happen that the end piers are not clear of the
+embankment slope, in which event a pier may, should the
+bank slip, move with it, as to that part not in solid ground;
+with the result, in a bad case, that it is broken across and the
+superstructure imperilled.</p>
+
+<div class="figcenter"><a name="Fig90" id="Fig90"></a>
+<img src="images/illo170.png" alt="" width="450" height="248" />
+<p class="caption"><span class="smcap">Fig.</span> 90.</p>
+</div>
+
+<p>A case of abutment movement is illustrated in <a href="#Fig90">Fig. 90</a>,
+which represents the end arch of a masonry viaduct, one
+abutment of which had moved forward in the manner
+already referred to. From the springing upwards the arch
+retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the
+movement became pronounced, heavy timber centering was
+introduced, with the object of preventing any mishap, the
+damaged portions being ultimately cut out and made good.
+The structure was thirty-five years old.</p>
+
+<p>The practical utility of stop piers in long arched viaducts
+is, perhaps, rather in checking movement of the tops of piers<span class="pagenum"><a name="Page_159" id="Page_159">[159]</a></span>
+under moving load than in arresting actual failure of a series
+of arches. That the tops of piers do move very sensibly
+need not be doubted. The author has attempted to measure
+this in the case of piers about 60 feet to the springing, by
+means of a theodolite placed below, but has reached no more
+definite result than that a movement existed, of which he
+was not able to determine the amount. If in a viaduct some
+arches are more heavily loaded than others, each spreading
+slightly, the end piers of the group will move amounts which
+together equal the sum of the individual span spreads, with
+a tendency in the arches beyond those of the group overloaded
+to rise.</p>
+
+<p>This rocking may be detrimental both to the piers and
+arches, and helps to account for the disintegration of mortar
+in arches and piers, which not infrequently happens. The
+soffits will sometimes be seen with a thick incrustation of
+lime, which has washed out of the joints, or from limestone
+ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that
+pieces of stone or brick will drop out, necessitating repair at
+heavy expense, of which scaffolding is commonly a large
+part.</p>
+
+<p>Tall piers may be found badly out of the upright due to
+sinking of foundations. A marked case of this kind came
+under the author&#8217;s notice&mdash;a viaduct of fifteen semicircular
+arches, in which, though many piers were wanting in truth,
+one in particular was about 1 foot 4 inches out of vertical,
+making one side of the shaft plumb, and doubling the normal
+batter of the other. Inquiry showed that in this instance
+the pier had never been upright from its earliest history
+dating back thirty-six years. This makes clear the desirability,
+to avoid hasty conclusions, of ascertaining, when it is
+possible to do so, the complete record of any structure.</p>
+
+<p>A bridge fifty-eight years old, of three skew spans, carrying<span class="pagenum"><a name="Page_160" id="Page_160">[160]</a></span>
+a railway over a canal, and having somewhat flat brick
+arches with stone quoins upon low piers, developed the somewhat
+unusual defect, as to the centre arch, of splitting along
+its length for about 10 feet, parallel to and some 7 feet from
+one face. In this case there was reason to believe that there
+had been considerable local settlement of the piers on that
+side of the bridge. The arches were otherwise in bad condition,
+the brickwork poor, and the mortar decayed. Each
+arch was down at the centre, and displayed a fault not
+unusual where bad brickwork joins up to good cut stonework,
+the quoins showing a tendency to separate from the
+brick rings. Below the bridge were coal-workings.</p>
+
+<p>Brick arches built in parallel rings sometimes separate
+one ring from the other, demonstrating the known propriety
+of bonding the rings together properly, and of carrying the
+arch round, when building, at its full thickness.</p>
+
+<div class="figcenter"><a name="Fig91" id="Fig91"></a>
+<img src="images/illo172.png" alt="" width="550" height="245" />
+<p class="caption"><span class="smcap">Fig.</span> 91.</p>
+</div>
+
+<p>An instance of bridge failure from a somewhat peculiar
+cause may be quoted as of some interest, largely because the
+structure was very ancient, having been in existence some
+400 years. This bridge, carrying a road, was of the type
+usual in old masonry bridges over a river, having small
+arches, thick piers, and solid backings to the arches. Two<span class="pagenum"><a name="Page_161" id="Page_161">[161]</a></span>
+flood-openings at one end had, by sinking and want of care,
+become partly closed. The centre arch had, however, been
+widened about 140 years previously. During a severe flood,
+the swollen river, overflowing its banks, trespassed upon a
+timber yard a little above bridge, and washed down into the
+stream a large quantity of sawn timber; this, unable to get
+through the main arch with freedom, compacted into a serious
+obstruction. The flood water, thus checked in its passage,
+seems to have scoured below the timber, and robbed the piers
+of such support as they formerly had (see <a href="#Fig91">Fig. 91</a>). The
+bridge stood in this condition till the water lowered, when
+the middle part of the structure broke up, and subsided into
+the hole which had been washed out. But for the monolithic
+character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers
+stood had been partly undermined
+for very many years.
+The case is instructive, as
+showing how a slight accident&mdash;powerless
+by itself
+to work mischief&mdash;may be
+very damaging when allied
+with so powerful an agent
+as running water.</p>
+
+<div class="figcenter"><a name="Fig92" id="Fig92"></a>
+<img src="images/illo173.png" alt="" width="300" height="351" />
+<p class="caption"><span class="smcap">Fig.</span> 92.</p>
+</div>
+
+<p>The enduring character
+of even the roughest class
+of masonry arch, if only
+the material be good and
+abutments stable, is shown
+when it becomes necessary to destroy old work of this
+character. <a href="#Fig92">Fig. 92</a> represents a short length of &#8220;cut and
+cover&#8221; arching in process of demolition, just before it
+fell in. The masonry was of hard sandstone rubble and
+had been cut away, as shown, till at the point A only a very<span class="pagenum"><a name="Page_162" id="Page_162">[162]</a></span>
+small piece of the arch remained, when the length finally
+broke up and dropped. Arches have commonly a great
+reserve of strength; tunnel linings are, indeed, often badly
+out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed
+or bulged, to serve the purpose intended.</p>
+
+<p>Though the equilibrium of masonry arches has been the
+occasion of much profound study, and the nicest calculation
+has sometimes been applied to the design of such work, yet
+it appears that when an arch is well backed up, the theoretical
+linear arch need have but little connection with the figure of
+the intrados; a statement consonant both with common-sense
+and the teachings of experience. With solid backing, this
+would indeed seem to be more important than any part of
+the arch ring below the top of the backing, the lower part
+of the ring serving chiefly to preserve the face of the solid
+work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure
+would seem to be inevitable. The masonry or brickwork
+does not always show evidence of damage, if the distortion
+has been slow; suggesting that structures of this kind have
+a power of accommodation with which they are not generally
+credited.</p>
+
+<p>A noticeable cause of deterioration of masonry structures,
+which may be quite independent of settlement, is serious
+vibration. This is well known in connection with church
+belfries, and is also locally apparent when telegraph or other
+poles are attached to masonry parapets. Vibration, when
+caused by heavy railway traffic, acting upon arches light or
+originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially
+built, and particularly those carrying ordinary roads,
+and not subject to much vibration, have great lasting powers,<span class="pagenum"><a name="Page_163" id="Page_163">[163]</a></span>
+if repaired with skill, or even let alone. Distortion of the
+arch may be quite consistent with practical stability, if the
+movement or decay with which it originated is not progressive,
+or has been arrested. In this connection a distinction
+is to be made between arches well backed, to which the foregoing
+remarks apply, and in which the two halves of each
+arch may act as separate monoliths meeting at the crown, and
+the case of a true arch ring independent of any outside resistance,
+such as backing or spandrels may give, and depending
+almost wholly upon the proper balance of its component
+voussoirs for its stability. With the latter class of structure
+no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way,
+and the work is dealt with judiciously, if at all. It must,
+however, be understood that there are limits as to what
+may be done effectively, short of rebuilding, in dealing with
+structures in which, perhaps, brickwork is rotten and mortar
+decayed and crumbling, the whole being little better than a
+broken mass of rubbish.</p>
+
+<p>In cases where it may be prudent to introduce safety
+centring, as in an instance already referred to, it is commonly
+expedient to refrain from causing this to take any sensible
+part of the load till all movement has ceased, the centres
+being at the outset largely precautionary. The requirement
+with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement
+is still going on, the effect may be to cause the arch to break
+up upon the centring, and precipitate repair work which
+might otherwise have been left to a more convenient time,
+when all movement had stopped or been checked by suitable
+measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt
+with piecemeal by cutting out the bad places, a small part<span class="pagenum"><a name="Page_164" id="Page_164">[164]</a></span>
+at a time, and making good. The work requires the greatest
+care of experienced men.</p>
+
+<p>Pointing masonry or brickwork is effective for little
+other than protective purposes, and to check further weathering;
+it has obviously no effect upon the interior work, and
+if made to cover up the evidences of internal decay, is even
+misleading and objectionable. In extreme cases it may be
+desirable to open out the road and deal with the filling, to
+relieve or to strengthen the outer spandrel walls, which sometimes
+bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise
+repairing solid backing, in which operations some regard
+must be had to the effect of the work upon the balance of
+the opposing halves of the arch.</p>
+
+<p>Of the different classes of masonry commonly used in
+bridgework, it may be well to remark that good coursed
+rubble, or preferably that variety bonding both vertically
+and horizontally, of a durable stone, perhaps quite unfit for
+any but rough dressing, may make a most lasting structure,
+the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from
+the block, probably along some line of relative weakness&mdash;there
+is no &#8220;nursing&#8221; of weak corners; whereas with stones
+reduced to a perfectly regular shape by chisel work, the
+plane surfaces and geometrical angles are made with partial
+regard only to the natural grain of the stone.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_165" id="Page_165">[165]</a></span></p>
+
+<h2>CHAPTER XV.<br />
+<span class="chaptitle">LIFE OF BRIDGES&mdash;RELATIVE MERITS.</span></h2>
+
+<p>The life of bridges of differing materials has been incidentally
+touched upon by the examples quoted, in dealing with
+each class of structure. It will be useful to recapitulate
+some of the facts adduced, and to compare the terms of life
+so far as they appear to be indicated; but in doing this it is
+necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history.
+The duration of any such structure may be limited by adverse
+conditions, peculiar to the case considered, by defects
+of design, material, or workmanship&mdash;present from the first&mdash;or
+by neglect, overloading, or accident, making up its later
+record.</p>
+
+<p>With the exception of timber structures, it is difficult to
+find any class of bridges furnishing examples which have
+reached the limit of life, independently of the evils named,
+and as a result of unavoidable decrepitude. There are none
+the less influences at work tending to this condition, and
+which it is too much to expect can in all cases be foreseen or
+completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and
+minor faults in design, which even in the most capable hands
+may be expected ever to fall short of perfection. At the
+best, then, the life of any structure, though long, must have
+a limit. With bridges of more average or inferior qualities
+the life may be positively short, even without the destructive
+influence of overloading.</p>
+
+<p><span class="pagenum"><a name="Page_166" id="Page_166">[166]</a></span></p>
+
+<p>Dealing with instances of metallic bridges, the adjacent
+table gives the time each had been in existence when removed,
+and some indication of the reason for its condemnation.
+Those marked with an asterisk were cases of pronounced high
+stress. From a study of the table it appears that in actual
+practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and
+thirty-six years; but these figures applied to this collection
+of cases only. It is to be remarked that many other bridges
+outlasted these, and are likely to continue reliable. These
+results show, then, no more than that some wrought-iron
+bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as
+indicating that the durability of such structures is by no
+means so limited as the table would suggest. It is to be
+observed that, as design and maintenance are now better and
+more generally understood than when experience was largely
+wanting, it is to be expected that later examples will show
+no such poor results.</p>
+
+<p>Of steel bridges little can be said, because of the limited
+time this material has been in use; but the generally acknowledged
+belief, quite in agreement with the author&#8217;s observation,
+that steel rusts more freely than wrought iron, suggests
+that such bridges will have a shorter lease of life, the more
+so that the surface-to-section ratio is also greater for higher
+unit stresses, though other adverse influences are much the
+same for one material as for the other.</p>
+
+<p>Of cast-iron structures but few cases have been given; of
+these, cast-iron arches have been noticed as developing defects
+which led to reconstruction, or to limiting the loads to be
+carried. Plain cast-iron girders, on the other hand, have
+never, under the author&#8217;s direct observation, been removed
+for any other reason than because they were cast iron, or
+from over-stress, due to the growth of loads; never from<span class="pagenum"><a name="Page_167" id="Page_167">[167]</a></span>
+defects or wasting, though it is not suggested no such cases
+exist. The author has no evidence which points to what
+may be the limit of life of a good cast-iron girder fairly
+treated.</p>
+
+<p class="center"><i>Examples of Life of Metallic Bridges.</i></p>
+
+<table class="nowrap" summary="Table page 167">
+
+<tr class="bt bb">
+<th class="center padl1 padr1 br">Description.</th>
+<th colspan="2" class="center padl1 padr1 br">Span.</th>
+<th class="center padl1 padr1 br">Age.</th>
+<th class="center padl1 padr1 br">Defect.</th>
+<th class="center padl1 padr1">Reference.</th>
+</tr>
+
+<tr>
+<th class="br">&nbsp;</th>
+<th class="center padl1 padr1">ft.</th>
+<th class="center padl1 padr1 br">in.</th>
+<th class="center padl1 padr1 br">Years.</th>
+<th class="br">&nbsp;</th>
+<th>&nbsp;</th>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Wrought Iron.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">12</td>
+<td class="center padl1 padr1 br">Loose rivets</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">*Ditto</td>
+<td class="right padl1 padr1">35</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">12</td>
+<td class="center padl1 padr1 br">Ditto</td>
+<td class="left padl1 padr1"><a href="#Page_52">p. 52</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">55</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">14</td>
+<td class="center padl1 padr1 br">Rust. Distortion</td>
+<td class="left padl1 padr1"><a href="#Page_78">pp. 78</a> &amp; <a href="#Page_97">97</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Trough girders</td>
+<td class="right padl1 padr1">11</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">16</td>
+<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_50">p. 50</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">22</td>
+<td class="center padl1 padr1 br">Loose rivets</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Twin girders</td>
+<td class="right padl1 padr1">31</td>
+<td class="right padl1 padr1 br">6</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Weak. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_13">p. 13</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">35</td>
+<td class="right padl1 padr1 br">6</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Weak. Distorted.</td>
+<td class="left padl1 padr1"><a href="#Page_74">p. 74</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Plate girders</td>
+<td class="right padl1 padr1">42</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">23</td>
+<td class="center padl1 padr1 br">Loose rivets. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_21">p. 21</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">72</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">29</td>
+<td class="center padl1 padr1 br">Weak. Loose rivets</td>
+<td class="left padl1 padr1"><a href="#Page_53">p. 53</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">47</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">24</td>
+<td class="center padl1 padr1 br">Distortion</td>
+<td class="left padl1 padr1"><a href="#Page_9">p. 9</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">32</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">32</td>
+<td class="center padl1 padr1 br">Rust. Cracked webs</td>
+<td class="left padl1 padr1"><a href="#Page_14">p. 14</a></td>
+</tr>
+
+<tr>
+<td class="left padl3 padr1 br">*Ditto</td>
+<td class="right padl1 padr1">25</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">36</td>
+<td class="center padl1 padr1 br">Weak</td>
+<td class="left padl1 padr1"><a href="#Page_63">p. 63</a></td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Steel.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">*Trough girders</td>
+<td class="right padl1 padr1">15</td>
+<td class="right padl1 padr1 br">8</td>
+<td class="center padl1 padr1 br">32</td>
+<td class="center padl1 padr1 br">Weak. Rusted</td>
+<td class="left padl1 padr1"><a href="#Page_68">pp. 68</a> &amp; <a href="#Page_98">98</a></td>
+</tr>
+
+<tr>
+<td colspan="6" class="center highline"><i>Cast Iron.</i></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br">*Girders</td>
+<td class="right padl1 padr1">32</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">36</td>
+<td class="center padl1 padr1 br">Weak</td>
+<td class="left padl1 padr1"><a href="#Page_141">p. 141</a></td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Girders, cast-iron piles</td>
+<td colspan="2" class="center padl1 br">(?)</td>
+<td class="center padl1 padr1 br">44</td>
+<td class="center padl1 padr1 br">Ditto</td>
+<td>&nbsp;</td>
+</tr>
+
+<tr>
+<td class="left padl1 padr1 br"><span class="noshow">*</span>Arches</td>
+<td class="right padl1 padr1">45</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">55</td>
+<td class="center padl1 padr1 br">Crack. Settlement</td>
+<td class="left padl1 padr1"><a href="#Page_145">p. 145</a></td>
+</tr>
+
+<tr class="bb">
+<td class="left padl3 padr1 br"><span class="noshow">*</span>Ditto</td>
+<td class="right padl1 padr1">100</td>
+<td class="right padl1 padr1 br">0</td>
+<td class="center padl1 padr1 br">62</td>
+<td class="center padl1 padr1 br">Crack. Deformation</td>
+<td class="left padl1 padr1"><a href="#Page_80">pp. 80</a> &amp; <a href="#Page_145">145</a></td>
+</tr>
+
+</table>
+
+<p>With timber bridges the length of life appears to be about
+twenty-five years, but this is very largely dependent upon
+the question of maintenance, and may range from fifteen to
+thirty-five years. It is manifest that repairs, when extensive
+and consisting of the renewal of the more essential parts of<span class="pagenum"><a name="Page_168" id="Page_168">[168]</a></span>
+the structure, border upon reconstruction, and may be continued
+indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for
+railway bridges, be taken as stated, though for highway
+bridges possibly longer.</p>
+
+<p>Of masonry bridges little is to be said but that it is only
+in cases of bad work or material&mdash;with, perhaps, vibration
+or settlement&mdash;that these have a shortness of life comparable
+with that of defective metallic bridges. Where these adverse
+conditions obtain, heavy repairs may be necessary before the
+structure is many years old; but, under reasonably fair conditions,
+bridges of masonry may be expected to outlast structures
+in any other material. Apart from road-bridges which
+are admittedly long-lived, there are a large number of railway
+bridges and viaducts of masonry which, despite heavy loads
+and vibration, have been in use for the past seventy years.</p>
+
+<p>Dealing with the cost of maintenance, this with bridges
+of wrought iron or steel should result simply from scraping
+and painting, with such other incidental work as may be
+necessary on the subsidiary materials used in the structure.
+The cost of painting will vary with the height and character
+of the bridge, and the amount of scaffolding, if any, and
+may be from 5<i>d</i>. to 1<i>s</i>. or more per square yard; this if
+distributed over five years, a not unusual interval between
+each painting, works out at an appreciable figure, which may
+vary from one-third to one per cent. of the first cost, per
+annum. The yearly cost of painting steel-work will, for
+shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be
+necessary, repairs and possibly strengthening, which may
+raise the total cost of maintenance very considerably.</p>
+
+<p>Cast-iron bridges, being less liable to rust, cost less for
+painting than other metallic bridges; and if the cast iron is
+closed in by masonry, practically nothing; they do, indeed,<span class="pagenum"><a name="Page_169" id="Page_169">[169]</a></span>
+involve very little expenditure in the maintenance. Not
+being very amenable to repair or strengthening, cast-iron
+bridges commonly remain very much as built, or are reconstructed.</p>
+
+<p>The proper care of timber bridges may become costly as
+the structure gains in age, and soon grow to a very wasteful
+expenditure. This is evident when it is considered that
+repairs may be necessary after ten years, and that whatever
+may have been the cost of any part when new, it cannot be
+replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions
+to be observed in dealing with an old structure
+carrying its load. In addition to ordinary repairs, there will
+be paint or other protective coating to be applied, though
+this is not always done.</p>
+
+<p>The upkeep charges of masonry bridges will be practically
+nothing in favourable cases; but, on the other hand, where
+extensive repairs become necessary, may reach a considerable
+amount. Exceptional outlays are, however, infrequent, and
+may be spread over a large number of years, in those rare
+instances in which they become imperative.</p>
+
+<table class="nowrap" summary="Table page 169">
+
+<tr>
+<th class="center"><i>Durability.</i></th>
+<th class="center padl3 padr3"><i>Maintenance<br />Charges.</i></th>
+<th class="center"><i>First Cost.</i></th>
+</tr>
+
+<tr>
+<td class="left">Masonry</td>
+<td class="left padl3 padr3">Masonry</td>
+<td class="left">Timber</td>
+</tr>
+
+<tr>
+<td class="left">Cast Iron</td>
+<td class="left padl3 padr3">Cast iron</td>
+<td class="left">Masonry</td>
+</tr>
+
+<tr>
+<td class="left">Wrought iron</td>
+<td class="left padl3 padr3">Wrought iron</td>
+<td class="left">Steel</td>
+</tr>
+
+<tr>
+<td class="left">Steel</td>
+<td class="left padl3 padr3">Steel</td>
+<td class="left">Cast iron</td>
+</tr>
+
+<tr>
+<td class="left">Timber</td>
+<td class="left padl3 padr3">Timber</td>
+<td class="left">Wrought iron</td>
+</tr>
+
+</table>
+
+<p>For purposes of ready comparison, placing bridges of the
+materials under review in order of durability, they would
+appear as in column 1 of the table above; in order of low
+maintenance charges, generally as in column 2; and in order
+of low first cost, as in column 3. With respect to the question
+of first cost, the arrangement of the third column applies
+only to small bridges, say, up to 70-foot span; and, being<span class="pagenum"><a name="Page_170" id="Page_170">[170]</a></span>
+liable to variation with the conditions, is but approximately
+correct. The less costly descriptions of masonry are alone
+considered in this connection.</p>
+
+<p>It may be added that the total yearly charge of interest
+on first cost, redemption, and maintenance, appears to be for
+masonry bridges, about one-half only of the corresponding
+totals for bridges of wrought iron, steel, or timber; those of
+cast iron taking an intermediate place.</p>
+
+<p>Summarising the above considerations, and dealing with
+the relative merits of bridges in the different materials, it
+may be broadly stated that for conditions at all suitable
+nothing seems to be superior to masonry&mdash;including in
+this description first-class brickwork&mdash;whether for road or
+railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little
+affected by increase of loads. The mass of a masonry arched
+structure is so great, and the margin of strength commonly
+so liberal, that considerable increments of load may have but
+little effect upon the reliability of the structure.</p>
+
+<p>Cast iron has, for bridges of simple design, a strong claim
+to the second place, though its want of ductility is a demerit.
+It can, however, have but a limited use in bridge construction,
+being applicable only to small girder spans and skilfully-designed
+arched structures.</p>
+
+<p>For bridges of moderate span in which the question of
+cost does not control the matter, wrought iron should probably
+come next, steel being best reserved for those of a larger
+size, in which weight of the structure greatly affects economy.</p>
+
+<p>Timber may be regarded as a material rarely to be used
+in this country for structures to occupy a permanent place,
+unless for urgent economic reasons of the moment.</p>
+
+<p>While expressing this general view of the matter, it is to
+be admitted that the propriety of these conclusions is somewhat
+discounted by the difficulty there now is in obtaining<span class="pagenum"><a name="Page_171" id="Page_171">[171]</a></span>
+cast iron of the desired toughness, or wrought iron with
+promptitude and sufficient variety of section at a reasonable
+price.</p>
+
+<p>It is apparent, also, that the choice of material may be
+largely influenced&mdash;even determined&mdash;by considerations of
+headway, construction depth, or character of foundations; so
+that no very definite rules can be usefully laid down, though
+the adoption of unsuitable materials has not been so unusual
+as to make these suggestions altogether purposeless.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_172" id="Page_172">[172]</a></span></p>
+
+<h2>CHAPTER XVI.<br />
+<span class="chaptitle">RECONSTRUCTION AND WIDENING&mdash;CONCLUSION.</span></h2>
+
+<p>The need for the reconstruction of bridges, arising from
+various causes which have been treated in the preceding
+chapters, original weakness or faults in design, decay or defects,
+may also be caused by such extraneous considerations as the
+growth of loads, widening of the openings spanned, or improvement
+of the headway.</p>
+
+<p>In any case, a precise survey or measuring up of the
+structure and its immediate surroundings is required, in the
+execution of which the greatest care is desirable, and with
+respect to which it may be well to give a few hints.</p>
+
+<p>The surveying chain, when used, should be tested, the
+measure of accuracy required rendering this imperative in a
+degree peculiar to work of this class. Linen tapes should
+also be compared with a reliable steel tape, and used only
+where sufficiently accurate for the particular purpose. A
+careful and observant man may do very good work with a
+linen tape, making just that allowance in the sag of the tape
+which corrects for the inevitable stretch; but there is still
+some uncertainty involved in its use, and the author prefers
+to rely upon a steel tape, notwithstanding the inconvenience
+commonly experienced from its intractable nature and liability
+to damage.</p>
+
+<p>Instruments used must also be in the best adjustment;
+as errors, which in ordinary field work may not be of great
+importance, are inadmissible in bridge work.</p>
+
+<p>It is not necessary here to enter upon the methods of<span class="pagenum"><a name="Page_173" id="Page_173">[173]</a></span>
+small survey work, but it may be desirable to point out that
+abutment walls should be plumbed for verticality; girders,
+which are liable to be leaning, defined in position by reference
+to their bearings; and generally that it should never be taken
+for granted that there is truth in old work, or that this may
+be assumed as to line or level.</p>
+
+<p>In cases where disputes with any local authority as to
+headway are likely to arise, it is prudent to supplement the
+information as to level of soffits by rods cut to length in strict
+agreement with the clear height, before removing the old
+superstructure.</p>
+
+<p>It is apparent that in cases where the superstructure is
+already condemned, the detail measurements may be confined
+to that part of the structure which is to remain, securing
+only such information as to the work superseded which may
+be required in arranging for the new work.</p>
+
+<p>In taking particulars of skew bridges, needless as the
+warning may seem, it is yet necessary to remark that there
+may be right or left-hand skews which will not reverse.
+The author has known a disregard of this to make serious
+trouble in two instances.</p>
+
+<p>Dealing first with reconstruction of the superstructure of
+railway under-bridges, these, if small, may not give much
+trouble, though the demand for greater strength will, perhaps,
+involve some difficulty in working to the limiting construction
+depth&mdash;i.e., the distance from the top of rail to soffit of
+bridge&mdash;particularly as many old bridges have a very niggardly
+allowance in this respect. It may be, and quite
+commonly is, necessary to raise the rails a small amount, or,
+if headway is not restricted, to lower the soffit. Clearances
+between the running gauge and girder-work may also be
+difficult to secure, more liberal allowances being now required
+than formerly. Complications in the character of the permanent
+way, so frequently found upon old bridges, should,<span class="pagenum"><a name="Page_174" id="Page_174">[174]</a></span>
+of course, be got rid of, if possible; but the endeavour may
+introduce further difficulties. Regard must throughout be
+had to the methods to be adopted in removing old work and
+in erecting the new. Perhaps the simplest case to deal with
+is that where girders lie parallel to, and under the rails, with
+a timber floor upon which the permanent way is carried, as
+sections of the road involving pairs of girders may be readily
+removed, and replaced by the new girder-work (see <a href="#Fig93">Fig. 93</a>).
+If the deck be of trough flooring or old rails, the matter may
+not be so simple, as regard must then be had to the position
+of joints in the existing floor, and the new work be schemed
+with respect to the number and office of girders which may
+be got in at any one breaking of the road. A slight slewing
+of rails may sometimes be resorted to on occasion, where this
+has the effect of releasing some part of the work not otherwise
+to be dealt with.</p>
+
+<div class="figcenter"><a name="Fig93" id="Fig93"></a><a name="Fig94" id="Fig94"></a>
+<img src="images/illo186.png" alt="" width="450" height="325" />
+<p class="caption"><span class="smcap">Figs.</span> 93 and 94.</p>
+</div>
+
+<p>Bridges having main girders, with timber or trough flooring
+resting upon the bottom flanges, or suspended by bolts,
+will, if carrying many roads, cause some little difficulty, as
+the dismantling of any one span involves the disturbance of<span class="pagenum"><a name="Page_175" id="Page_175">[175]</a></span>
+others; where, however, many lines are concerned, it may
+be feasible to put one or more temporarily out of use, preserving
+the continuity of traffic over those which remain,
+but refraining from any diversion of the more important
+roads.</p>
+
+<p>Somewhat similar troubles occur where main girders with
+cross-girders at the lower flanges are found, particularly if
+the cross-girders are arranged in line, the ends abutting on
+each side of the same main girder webs. It is seldom, however,
+that this construction is used in bridges of small span
+carrying many roads; but where it does occur, it may necessitate
+the use of timbering below, to carry the ends of cross-girders
+when freed from their supporting main girders.
+(See <a href="#Fig94">Fig. 94</a>.)</p>
+
+<div class="figcenter"><a name="Fig95" id="Fig95"></a>
+<img src="images/illo187.png" alt="" width="500" height="109" />
+<p class="caption"><span class="smcap">Fig.</span> 95.</p>
+</div>
+
+<p>If it is proposed to use new main and cross-girders, it is
+desirable to arrange these in the manner already recommended,
+the cross-girders not in line; this has peculiar advantages in
+reconstruction work, as the bolting up and riveting of the
+cross-girder ends is not hampered by other cross-girder
+attachments, leaving each piece of floor complete in itself.
+Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence
+of one span from those adjoining (see <a href="#Fig95">Fig. 95</a>);
+but the method is wasteful of space, and involves a somewhat
+greater total weight in the main girders.</p>
+
+<p>The foregoing observations apply more generally to small<span class="pagenum"><a name="Page_176" id="Page_176">[176]</a></span>
+single-span bridges, the operations on which may be effected
+without any material disturbance of traffic arrangements;
+though this can seldom be wholly avoided, it should be confined,
+where practicable, to a few hours on a Sunday.</p>
+
+<p>The reconstruction of bridges over 70-feet span may have
+to be dealt with under more elaborate arrangements, if carrying
+two lines only, possibly with single-line working for a
+period more or less protracted; or it may be necessary, having
+regard to the weight of main girders to be removed, to carry
+the whole structure upon temporary staging, supporting the
+road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed
+erection in its ultimate position, or by erection at one side
+and drawing across. The latter method is, however, commonly
+reserved for cases in which no special staging is used
+under the old structure.</p>
+
+<p>Bridges of a number of openings are usually dealt with
+by securing full possession of one road at a time, which for
+double-line bridges necessitates single-line working. It is
+commonly out of the question, even with moderate spans,
+to deal with some of these only at a time, and so avoid continuous
+possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new
+main girders do not in any way interfere with those of the
+old, and where it is not necessary to reset bed-stones, or make
+other alterations in the bearings which necessitate the complete
+clearance of the pier-tops. In exceptional cases it may
+be found possible to arrange for the complete removal of a
+small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.</p>
+
+<p>Spans erected to one side of the final position, to be later
+travelled across, are commonly mounted upon gantry staging,
+and up to 50 tons weight may rest directly upon rails well
+greased. The power adopted to move the span is usually<span class="pagenum"><a name="Page_177" id="Page_177">[177]</a></span>
+that of screw or hydraulic jacks, or occasionally engine haulage,
+special tackle being in that case necessary to apply the
+engine power in the right direction. If the time is limited,
+or weight considerable, a more elaborate arrangement by
+which the load is supported upon wheels, may be necessary,
+with a view to reducing the resistance to a manageable
+amount. All work which it is possible to do before shifting
+into place, including the permanent way, where this is of a
+special character, should be executed in advance, leaving only
+the rail connections to be made good when the span is in
+position.</p>
+
+<p>Where timber staging is used to carry the permanent
+way before dismantling an old structure, it is convenient to
+begin by placing stout balks of timber under the sleepers
+from end to end of the bridge, or directly under the rails if
+space is limited; the staging is then arranged to give support
+to the running timbers.</p>
+
+<p>Metallic under-bridges of ample headway, perhaps over
+coal-workings (since settled down), or for some less sufficient
+reason made of metal, may be cheaply replaced by brick
+arches built below the old superstructure, the springings of
+the arch being checked into the face of the existing abutments.
+With stout walls, careful work and good material will make
+this an efficient and durable job.</p>
+
+<p>It being a primary condition of reconstruction work to
+interfere but little with ordinary traffic arrangements, single-line
+working is avoided wherever practicable; as this, always
+objectionable, may necessitate the erection of special signals
+and signal apparatus, besides the temporary remodelling of
+the roads, and in this country may involve also a Board of
+Trade inspection&mdash;altogether a troublesome and expensive
+business.</p>
+
+<p>Any bridgework which is accompanied by breaking or
+blocking the road can only be undertaken by arrangement<span class="pagenum"><a name="Page_178" id="Page_178">[178]</a></span>
+with the traffic department, after notice duly given and
+published in the periodical record of such matters; it is
+generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand
+as is possible. Wherever practicable and prudent, the
+whole work is released from its surroundings, masonry cut
+away, rivets cut out and replaced by good bolts, nuts removed
+from holding down bolts, or the bolts cut through, etc.
+Particular care should be exercised to ascertain what remains
+to be done immediately prior to removal. It is necessary
+further to arrange for trucks to be in readiness to receive old
+material, and others containing new girder work to be conveniently
+stationed, having been loaded up to come right end
+foremost; engine power, cranes, empty and loaded trucks,
+being all marshalled and so placed as to be available in proper
+order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or
+as to the reach of the crane in effecting its work.</p>
+
+<p>The whole operation to be conducted on any Sunday
+should be well within the resources of the men and plant
+engaged in it, or so managed that it is a matter of no serious
+importance if the whole cannot be completed as originally
+desired.</p>
+
+<p>Possession of the roads to be blocked having been secured
+between certain hours, if some part only of the work to be
+carried out has been completed as the time grows short, any
+attempt to execute the remainder may result in checking
+trains until such time as the line may be reported clear&mdash;a
+contingency to be avoided&mdash;though the temptation to save
+another Sunday&#8217;s work by delay of a few minutes to some
+one train may be considerable.</p>
+
+<p>In scheming any reconstruction, it may be insisted that
+at least one feasible method of carrying out the work must
+be secured, though it is the author&#8217;s experience that frequently<span class="pagenum"><a name="Page_179" id="Page_179">[179]</a></span>
+some other method than that contemplated is in the end
+adopted, when, some months later, the final arrangements
+for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered,
+with a view to a moderate amount of work being done at any
+one time, and to achieve as much more as he can himself
+secure by scheming, or a liberal use of labour; all Sunday
+work, with attendance of engines and cranes, being of necessity
+expensive.</p>
+
+<p>Railway over-bridges do not commonly present any
+particular difficulties. The spans to be dealt with are
+usually small, and the weights to be lifted moderate. The
+height above rails may, however, be above the lift of any
+crane; and, for the purpose of raising main girders, a derrick
+may become necessary, the rearing and guying of which may
+block many roads during the time it is in use. The girders
+of larger spans, too unmanageable to be lifted whole, may
+be erected upon staging; to secure the requisite headway
+it may be necessary to build the girders at a level above
+that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the
+staging.</p>
+
+<p>The widening of railway under-bridges is, as a rule, a
+matter of no special difficulty, but some remarks may be of
+use. Widenings should be planned with a regard to later
+reconstruction of the original bridge, if that is at all likely
+to be necessary, and with the object that, when complete,
+the whole should be a consistent piece of work.</p>
+
+<p>It may, indeed, happen that widening of a bridge may
+involve the remodelling or reconstruction of the old work,
+to enable the new roads to be laid down as desired; this is
+more likely to be necessary where there exist main girders
+not competent to take any additional load, and to duplicate
+which would sacrifice space between the new and old roads;<span class="pagenum"><a name="Page_180" id="Page_180">[180]</a></span>
+or it may be unavoidable because of slewing of the old rails,
+as part of a general rearrangement.</p>
+
+<div class="figcenter"><a name="Fig96" id="Fig96"></a>
+<img src="images/illo192.png" alt="" width="450" height="195" />
+<p class="caption"><span class="smcap">Fig.</span> 96.</p>
+</div>
+
+<p>Dealing with widenings simply, there is often some little
+trouble in contriving a connection between the new and the
+old work, as this may have to be made under, or close to, the
+sleeper ends of the existing roads. It is desirable to arrange
+this part so that no drilling of old work for rivets or bolts
+shall be necessary, there being, in fact, no strict connection.
+By judicious scheming, this may be effected, whilst securing
+freedom from leakage of water at the joint. (See <a href="#Fig96">Figs. 96</a>
+and <a href="#Fig97">97</a>.) If tying of the new and old structure is desired,
+this can usually be done quite simply, well below the floor at
+some more accessible level.</p>
+
+<div class="figcenter"><a name="Fig97" id="Fig97"></a><a name="Fig98" id="Fig98"></a>
+<img src="images/illo193.png" alt="" width="350" height="453" />
+<p class="caption"><span class="smcap">Figs.</span> 97 and 98.</p>
+</div>
+
+<p>The strict jointing-up of trough flooring, new to old, at
+right angles to the troughs, cannot be contemplated, but may
+be dealt with by treating each part independently, the ends
+being near together, separated by the space of an inch or so.
+Each trough end being closed up by a diaphragm or oak
+block to prevent ballast dropping through, the top of the
+space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions
+to take away leakage, as it is practically impossible to
+make this arrangement &#8220;drop dry&#8221; under the conditions
+common in executing work of this kind (see <a href="#Fig98">Fig. 98</a>).</p>
+
+<p><span class="pagenum"><a name="Page_181" id="Page_181">[181]</a></span></p>
+
+<div class="figcenter"><a name="Fig99" id="Fig99"></a><a name="Fig100" id="Fig100"></a>
+<img src="images/illo194.png" alt="" width="350" height="375" />
+<p class="caption"><span class="smcap">Figs.</span> 99 and 100.</p>
+</div>
+
+<p>Where trough flooring, new and old, has to be made good
+parallel to the troughs, the difficulty of making a direct connection
+is less marked, and it is not unusual to introduce a
+strip cover simply; but if accessible, the work is still troublesome,
+as there is commonly a want of strict alignment and
+truth as to level, between the new and the old troughs. It
+is preferable to arrange for junctions of a more convenient
+type, as in <a href="#Fig99">Figs. 99 and 100</a>.</p>
+
+<p>When widening masonry arch bridges by girder-work, it
+is desirable to insure that any girders parallel to the masonry
+face shall be sufficiently far removed from it to enable painting
+to be executed. The space remaining between the girder
+and the arch may then be bridged by floor-plates, or an extension
+of the timber floor if that is adopted.</p>
+
+<p><span class="pagenum"><a name="Page_182" id="Page_182">[182]</a></span></p>
+
+<div class="figcenter"><a name="Fig101" id="Fig101"></a><a name="Fig102" id="Fig102"></a>
+<img src="images/illo195.png" alt="" width="350" height="529" />
+<p class="caption"><span class="smcap">Figs.</span> 101 and 102.</p>
+</div>
+
+<div class="figcenter"><a name="Fig103" id="Fig103"></a>
+<img src="images/illo196.png" alt="" width="300" height="289" />
+<p class="caption"><span class="smcap">Fig.</span> 103.</p>
+</div>
+
+<p>In effecting a junction such as this, the author has used
+the arrangement shown in <a href="#Fig101">Fig. 101</a>, the advantage being
+that the piece of connecting-floor is sufficiently wide, and
+also sufficiently flexible, to allow the girder-work freedom to
+deflect without doing harm. The load carried by the width
+of floor is, as to one part, delivered well on to the old
+masonry, in preference to being imposed near to the face.
+If it should for any reason be imperative to place the girder
+close to the arch face, it is preferable to scheme the floor so
+that there shall be no actual contact, the new floor in that
+case slightly overhanging the masonry, as in <a href="#Fig102">Fig. 102</a>, or
+dealt with as in <a href="#Fig103">Fig. 103</a>, if depth is restricted.</p>
+
+<p>The widening of masonry arch bridges by masonry, calls
+for no other remark than that the new work should be free
+from the old; though it may be advisable, when the widening<span class="pagenum"><a name="Page_183" id="Page_183">[183]</a></span>
+is narrow, to tie the new work to the old in such a way as
+to permit independent settlement.</p>
+
+<p>If the widening is exceptionally narrow, there may be
+no choice but to bond the new and old work together, and
+in the best manner, with the object of minimising the risk
+of separation.</p>
+
+<p>The above matters relative to widenings, though apparently
+trifling, may by neglect cause much trouble and expense
+in maintenance. They principally concern small bridges,
+the extension of larger structures coming rather in the category
+of independent works.</p>
+
+<p><span class="pagenum"><a name="Page_184" id="Page_184">[184]</a></span></p>
+
+<h3><span class="smcap">Conclusion.</span></h3>
+
+<p>In bringing these chapters, dealing largely with questions
+affecting maintenance, to a close, it may be well to draw
+attention to the fact that economy in design (apart from
+improper reduction of sections) goes hand-in-hand with
+economy of upkeep. Given good material, that which favours
+low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to
+girders, favours also small expenditure in maintenance.
+The less complex the design, the easier will it be to keep the
+structure in order; the less the number of parts, the fewer
+will be the connections. Freedom from smithing eliminates
+liability to failure at cranks, or other work which has been
+subject to fire. It is apparent also that the free use of rolled
+instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A
+liberal depth to all girders, by reducing deflections, limits the
+inclination of the ends and gives the connections a better
+chance of remaining intact. Lastly, with work of this
+character, the labour of scraping and painting is simplified
+and cheapened.</p>
+
+<p><span class="pagenum"><a name="Page_185" id="Page_185">[185]</a></span></p>
+
+<p>The author wishes to reiterate the statement made in
+the opening paragraphs of this book, that all instances of
+decrepitude, failure, or peculiar behaviour cited, have been
+under his direct observation. The fact is insisted upon
+simply that the reader may appreciate that the information
+is at first hand.</p>
+
+<p>It has not been thought necessary, nor was it considered
+desirable, to indicate the locality of each case referred to;
+but it may be said that the matter of these chapters has been
+accumulating during many years, and relates to structures
+under the control of many different bodies.</p>
+
+<p>The study of old bridges is strongly recommended,
+particularly with respect to stress and strain, which in structures
+new or old, occur possibly as may be expected&mdash;certainly
+as they must. Consideration of existing work may thus be a
+useful check upon the fanciful requirements of some methods
+of design. There is a recent tendency, for instance, in English
+practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many
+old bridges carrying their loads with no sign of distress, should
+have failed long ago. Excess in riveting is a common extravagance,
+to which the same criticism may in a less degree
+apply. Considerable impact allowances for girders of large
+span may also be referred to as an application of empiric
+theory not justified by experience, which, as in all cases
+where such considerations fight with facts, should be modified
+or rejected.</p>
+
+<hr class="chap" />
+
+<p><span class="pagenum"><a name="Page_186" id="Page_186"></a><br /><a name="Page_187" id="Page_187">[187]</a></span></p>
+
+<h2>INDEX</h2>
+
+<ul class="index">
+<li class="first">Abutments, leaning, <a href="#Page_82">82</a>, <a href="#Page_173">173</a></li>
+<li>&mdash; movements of, <a href="#Page_158">158</a></li>
+<li>&mdash; settlement of, <a href="#Page_78">78</a></li>
+<li>Adjustment of centre girders, <a href="#Page_128">128</a></li>
+<li>&mdash; of distributing girders, <a href="#Page_120">120</a></li>
+<li>Angular distortions, <a href="#Page_88">88</a></li>
+<li>Arches, equilibrium of, <a href="#Page_162">162</a></li>
+<li>&mdash; repair of, <a href="#Page_163">163</a></li>
+<li>Arrangement of cross girders, <a href="#Page_21">21</a>, <a href="#Page_175">175</a></li>
+<li>Asphalt, <a href="#Page_26">26</a></li>
+<li class="first">Ballast, <a href="#Page_29">29</a></li>
+<li>Bearing pressure on rivets, <a href="#Page_47">47</a>, <a href="#Page_51">51</a>, <a href="#Page_57">57</a></li>
+<li>Bearings, skew, <a href="#Page_4">4</a></li>
+<li>Bottom booms, end bays, <a href="#Page_18">18</a></li>
+<li>Bracing, additional, <a href="#Page_117">117</a></li>
+<li>&mdash; effects of, <a href="#Page_34">34</a></li>
+<li>&mdash; flat bars, <a href="#Page_37">37</a></li>
+<li>&mdash; incomplete, <a href="#Page_41">41</a></li>
+<li>&mdash; sea piers, <a href="#Page_42">42</a></li>
+<li>Bridge floors, <a href="#Page_20">20</a></li>
+<li>&mdash; repairs, <a href="#Page_107">107</a></li>
+<li>&mdash; surveys, <a href="#Page_107">107</a></li>
+<li>Bridges, life of, <a href="#Page_165">165</a></li>
+<li>Breaks in <span class="lettsymb">T</span> bars, <a href="#Page_16">16</a></li>
+<li>Buckling of webs, <a href="#Page_16">16</a></li>
+<li class="first">Camber, <a href="#Page_24">24</a>, <a href="#Page_80">80</a></li>
+<li>Cast-iron arches, <a href="#Page_80">80</a>, <a href="#Page_145">145</a></li>
+<li>&mdash; &mdash; bridges, <a href="#Page_141">141</a></li>
+<li>&mdash; &mdash; columns, <a href="#Page_7">7</a>,144</li>
+<li>&mdash; &mdash; girders, <a href="#Page_141">141</a></li>
+<li>&mdash; &mdash; in sea water, <a href="#Page_101">101</a></li>
+<li>Centre girders, <a href="#Page_122">122</a></li>
+<li>Cinder ballast, <a href="#Page_29">29</a></li>
+<li>Cold-blast iron, <a href="#Page_141">141</a></li>
+<li>Cooling stresses in cast iron, <a href="#Page_145">145</a></li>
+<li>Construction depth, <a href="#Page_173">173</a></li>
+<li>Corrugated sheeting, <a href="#Page_29">29</a></li>
+<li>Cost of centre girders, <a href="#Page_135">135</a></li>
+<li>&mdash; of maintenance, <a href="#Page_168">168</a></li>
+<li>Counterbracing, <a href="#Page_19">19</a></li>
+<li>Cracked bedstones, <a href="#Page_3">3</a></li>
+<li>&mdash; columns, <a href="#Page_7">7</a></li>
+<li>&mdash; web plates, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>Cross girder arrangement, <a href="#Page_21">21</a></li>
+<li>&mdash; girders, fixed ends, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li>
+<li>&mdash; &mdash; rusted, <a href="#Page_29">29</a>, <a href="#Page_97">97</a></li>
+<li>&mdash; &mdash; weak, <a href="#Page_30">30</a>, <a href="#Page_66">66</a></li>
+<li class="first">Decay and painting, <a href="#Page_96">96</a></li>
+<li>&mdash; of floor plates, <a href="#Page_109">109</a></li>
+<li>&mdash; of timber, <a href="#Page_28">28</a>, <a href="#Page_150">150</a></li>
+<li>Deflection, <a href="#Page_85">85</a></li>
+<li>&mdash; due to booms and web, <a href="#Page_86">86</a></li>
+<li>&mdash; exceptional cases, <a href="#Page_88">88</a></li>
+<li>&mdash; in new and old work, <a href="#Page_85">85</a></li>
+<li>&mdash; working formul&aelig;, <a href="#Page_87">87</a></li>
+<li>Deformations, <a href="#Page_73">73</a></li>
+<li>Depth of girders,<span class="pagenum"><a name="Page_188" id="Page_188">[188]</a></span> <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li>
+<li>Diagonal ties, <a href="#Page_19">19</a>, <a href="#Page_42">42</a></li>
+<li>Distortion due to temperature changes, <a href="#Page_79">79</a>, <a href="#Page_84">84</a></li>
+<li>Distributing girders, <a href="#Page_120">120</a></li>
+<li>Drainage holes, <a href="#Page_25">25</a></li>
+<li>&#8220;Drop&#8221; loads, <a href="#Page_89">89</a></li>
+<li>Dwarf walls under floors, <a href="#Page_26">26</a></li>
+<li class="first">Early steel girders, <a href="#Page_68">68</a></li>
+<li>Economy, <a href="#Page_184">184</a></li>
+<li>Effect of earth slips, <a href="#Page_157">157</a></li>
+<li>&mdash; of floor on deflection, <a href="#Page_88">88</a></li>
+<li>&mdash; &mdash; &mdash; on stresses, <a href="#Page_23">23</a>, <a href="#Page_30">30</a></li>
+<li>&mdash; of high stress, <a href="#Page_86">86</a></li>
+<li>&mdash; of permanent way on stresses, <a href="#Page_18">18</a></li>
+<li>&mdash;of skew on bridge floors, <a href="#Page_25">25</a></li>
+<li>&mdash; &mdash; &mdash; on centre girders, <a href="#Page_131">131</a></li>
+<li>&mdash; of transverse bracings, <a href="#Page_34">34</a></li>
+<li>&mdash; of vibration on masonry, <a href="#Page_162">162</a></li>
+<li>&mdash; of wave action on sea piers, <a href="#Page_42">42</a></li>
+<li>End bays, bottom booms, <a href="#Page_18">18</a></li>
+<li>Equilibrium of masonry arches, <a href="#Page_162">162</a></li>
+<li>Examination of bridges, <a href="#Page_107">107</a></li>
+<li>Examples of cast-iron bridges overstressed, <a href="#Page_141">141</a></li>
+<li>&mdash; of high stress, <a href="#Page_70">70</a></li>
+<li>&mdash; of life of bridges, <a href="#Page_167">167</a></li>
+<li>&mdash; of rivet stress, <a href="#Page_56">56</a></li>
+<li>&mdash; of strengthening, <a href="#Page_114">114</a></li>
+<li>&mdash; &mdash; &mdash; by centre girders, <a href="#Page_131">131</a>, <a href="#Page_134">134</a></li>
+<li>Excessive bearing pressure, <a href="#Page_51">51</a></li>
+<li class="first">Faulty workmanship, <a href="#Page_80">80</a></li>
+<li>Fixed ends to cross girders, <a href="#Page_22">22</a>, <a href="#Page_118">118</a></li>
+<li>Flange stresses, <a href="#Page_63">63</a>, <a href="#Page_66">66</a>, <a href="#Page_67">67</a></li>
+<li>Flanges, side loaded, <a href="#Page_9">9</a>, <a href="#Page_73">73</a></li>
+<li>Flat bar bracing, <a href="#Page_37">37</a></li>
+<li>Flexing of girders, <a href="#Page_9">9</a>, <a href="#Page_74">74</a>, <a href="#Page_76">76</a></li>
+<li>Flexure curves, <a href="#Page_138">138</a></li>
+<li>Fractured bedstones, <a href="#Page_3">3</a></li>
+<li>&mdash; rails, <a href="#Page_30">30</a></li>
+<li>&mdash; webs, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>Fractures in cast iron, <a href="#Page_7">7</a>, <a href="#Page_145">145</a></li>
+<li class="first">Girder bearings, <a href="#Page_2">2</a></li>
+<li>Girders on columns, <a href="#Page_7">7</a></li>
+<li>&mdash; on masonry, <a href="#Page_8">8</a></li>
+<li>Girderwork in masonry, <a href="#Page_101">101</a></li>
+<li class="first">Headway, <a href="#Page_173">173</a></li>
+<li>High stress, <a href="#Page_61">61</a></li>
+<li>&mdash; in cast iron, <a href="#Page_141">141</a></li>
+<li>&mdash; in rivets, <a href="#Page_47">47</a>, <a href="#Page_52">52</a></li>
+<li>Holes for drainage, <a href="#Page_25">25</a></li>
+<li class="first">Impact, <a href="#Page_20">20</a>, <a href="#Page_62">62</a></li>
+<li>Inclination of girder ends, <a href="#Page_23">23</a>, <a href="#Page_53">53</a></li>
+<li>Incomplete bracing, <a href="#Page_41">41</a></li>
+<li>Initial set, <a href="#Page_88">88</a></li>
+<li>Interference with traffic, <a href="#Page_177">177</a></li>
+<li class="first">Jack arches, <a href="#Page_29">29</a>, <a href="#Page_101">101</a></li>
+<li>Joints in rails, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li>
+<li>&mdash; in trough floors, <a href="#Page_28">28</a>, <a href="#Page_180">180</a></li>
+<li>Junction between metallic and masonry bridges, <a href="#Page_183">183</a></li>
+<li>&mdash; &mdash; new and old masonry bridges, <a href="#Page_182">182</a></li>
+<li>&mdash; &mdash; new and old metallic bridges, <a href="#Page_180">180</a></li>
+<li class="first">Lattice girder stresses, <a href="#Page_47">47</a>-<a href="#Page_66">66</a></li>
+<li>Liberal depth to girders, <a href="#Page_23">23</a>, <a href="#Page_89">89</a>, <a href="#Page_184">184</a></li>
+<li>Life of bridges,<span class="pagenum"><a name="Page_189" id="Page_189">[189]</a></span> <a href="#Page_165">165</a></li>
+<li>Limit of elasticity, <a href="#Page_61">61</a></li>
+<li>Linen tapes, <a href="#Page_172">172</a></li>
+<li>Longitudinal floor girders, <a href="#Page_23">23</a></li>
+<li>Loose rivets, <a href="#Page_21">21</a>, <a href="#Page_25">25</a>, <a href="#Page_51">51</a>, <a href="#Page_53">53</a>, <a href="#Page_56">56</a>, <a href="#Page_109">109</a></li>
+<li class="first">Main girders, <a href="#Page_9">9</a>-<a href="#Page_17">17</a></li>
+<li>Masonry bridges, <a href="#Page_157">157</a></li>
+<li>&mdash; enduring character of, <a href="#Page_161">161</a></li>
+<li>Memel timber, <a href="#Page_150">150</a></li>
+<li>Methods of calculation, <a href="#Page_46">46</a>, <a href="#Page_61">61</a></li>
+<li>&mdash; of observing deflection, <a href="#Page_90">90</a></li>
+<li>&mdash; of setting out deflection curves, <a href="#Page_138">138</a></li>
+<li>Movements of abutments, <a href="#Page_158">158</a></li>
+<li>&mdash; of cast-iron bridge, <a href="#Page_82">82</a></li>
+<li>&mdash; of piers, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>&mdash; of rollers, <a href="#Page_7">7</a></li>
+<li>&mdash; of wrought-iron bridges, <a href="#Page_4">4</a>, <a href="#Page_21">21</a>, <a href="#Page_38">38</a>, <a href="#Page_73">73</a></li>
+<li class="first">New members to old work, <a href="#Page_116">116</a></li>
+<li class="first">Oiling steelwork, <a href="#Page_99">99</a></li>
+<li>Old drawings unreliable, <a href="#Page_108">108</a></li>
+<li>&mdash; rivets, <a href="#Page_21">21</a>, <a href="#Page_51">51</a>, <a href="#Page_54">54</a>, <a href="#Page_55">55</a></li>
+<li>Open webs, <a href="#Page_17">17</a></li>
+<li>Overhead bracing, <a href="#Page_39">39</a></li>
+<li>&mdash; girders, <a href="#Page_118">118</a></li>
+<li class="first">Painting, <a href="#Page_98">98</a></li>
+<li>Parapets, <a href="#Page_79">79</a></li>
+<li>Permissible stress in old work, <a href="#Page_110">110</a></li>
+<li>Piers, movements of, <a href="#Page_42">42</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>&mdash; out of plumb, <a href="#Page_159">159</a></li>
+<li>Piles, decay of, <a href="#Page_102">102</a>, <a href="#Page_150">150</a></li>
+<li>Pitch pine, <a href="#Page_28">28</a></li>
+<li>Plasticity, <a href="#Page_61">61</a></li>
+<li>Plate webs, <a href="#Page_9">9</a></li>
+<li>Plated floors, <a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_30">30</a></li>
+<li>Pointing masonry, <a href="#Page_164">164</a></li>
+<li>Proposed rivet stresses, <a href="#Page_58">58</a></li>
+<li class="first">Quickly applied loads, <a href="#Page_89">89</a></li>
+<li class="first">Rail joints, <a href="#Page_29">29</a>, <a href="#Page_109">109</a></li>
+<li>Rails, breaks in, <a href="#Page_30">30</a></li>
+<li>Reaction of cross girder with centre support, <a href="#Page_127">127</a></li>
+<li>Red-lead, <a href="#Page_98">98</a>, <a href="#Page_100">100</a></li>
+<li>Relative merits of bridges, <a href="#Page_169">169</a></li>
+<li>Relief by centre girders, <a href="#Page_122">122</a></li>
+<li>Repainting, <a href="#Page_100">100</a></li>
+<li>Repair of bridges, <a href="#Page_107">107</a>, <a href="#Page_147">147</a>, <a href="#Page_155">155</a>, <a href="#Page_163">163</a></li>
+<li>&mdash; of timber piles, <a href="#Page_156">156</a></li>
+<li>Replacing flange plates, <a href="#Page_110">110</a></li>
+<li>&mdash; rivets, <a href="#Page_111">111</a></li>
+<li>Resistance of cast iron to rust, <a href="#Page_101">101</a></li>
+<li>Riveted connections, <a href="#Page_45">45</a>, <a href="#Page_86">86</a></li>
+<li>Rivets in cramped positions, <a href="#Page_20">20</a></li>
+<li>&mdash; in cross girder ends, <a href="#Page_21">21</a>, <a href="#Page_49">49</a>, <a href="#Page_53">53</a>, <a href="#Page_54">54</a></li>
+<li>&mdash; in road bridges, <a href="#Page_60">60</a></li>
+<li>&mdash; in webs of main girders, <a href="#Page_46">46</a></li>
+<li>&mdash; spacing of, <a href="#Page_60">60</a>, <a href="#Page_80">80</a></li>
+<li>&mdash; stresses in, <a href="#Page_56">56</a></li>
+<li>Rocking of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+<li>Roller bearings, <a href="#Page_7">7</a></li>
+<li>Rubble masonry, <a href="#Page_161">161</a>-<a href="#Page_164">164</a></li>
+<li>Running load and deflection, <a href="#Page_95">95</a></li>
+<li>Rusting, instances of, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li>
+<li>&mdash; of steelwork, <a href="#Page_99">99</a></li>
+<li>&mdash; over sea-water, <a href="#Page_98">98</a></li>
+<li class="first">Sag in timber bridges, <a href="#Page_150">150</a></li>
+<li>&mdash; of tapes, <a href="#Page_172">172</a></li>
+<li>Scour under piers,<span class="pagenum"><a name="Page_190" id="Page_190">[190]</a></span> <a href="#Page_161">161</a></li>
+<li>Sea piers, <a href="#Page_42">42</a>, <a href="#Page_102">102</a></li>
+<li>Setting bedstones, <a href="#Page_3">3</a>, <a href="#Page_129">129</a>, <a href="#Page_176">176</a></li>
+<li>Settlements, <a href="#Page_76">76</a>, <a href="#Page_157">157</a></li>
+<li>Skew bearings, <a href="#Page_4">4</a></li>
+<li>&mdash; bridges, right and left, <a href="#Page_173">173</a></li>
+<li>&mdash; &mdash; floors, <a href="#Page_25">25</a></li>
+<li>Skirting plate, <a href="#Page_26">26</a></li>
+<li>Slope of girder ends, <a href="#Page_92">92</a></li>
+<li>Softening of cast-iron in sea-water, <a href="#Page_101">101</a></li>
+<li>Spacing of rivets, <a href="#Page_60">60</a>, <a href="#Page_79">79</a></li>
+<li>Spread of abutments, <a href="#Page_157">157</a></li>
+<li>Spring joints, <a href="#Page_23">23</a></li>
+<li>Steel trough girders, <a href="#Page_68">68</a></li>
+<li>&mdash; troughing, <a href="#Page_70">70</a></li>
+<li>Stiffening girders from floor, <a href="#Page_12">12</a>, <a href="#Page_40">40</a></li>
+<li>&mdash; to webs, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li>
+<li>Stop piers, <a href="#Page_158">158</a></li>
+<li>Strength of light top booms, <a href="#Page_40">40</a></li>
+<li>Strengthening of bridges, <a href="#Page_107">107</a>, <a href="#Page_122">122</a></li>
+<li>&mdash; bridge floors, <a href="#Page_118">118</a></li>
+<li>&mdash; cross girders, <a href="#Page_123">123</a></li>
+<li>Stress in plated floors, <a href="#Page_31">31</a></li>
+<li>Study of old bridges, <a href="#Page_185">185</a></li>
+<li class="first">Tall piers, <a href="#Page_42">42</a>, <a href="#Page_159">159</a></li>
+<li>Timber bridges, <a href="#Page_149">149</a></li>
+<li>&mdash; floors, <a href="#Page_27">27</a></li>
+<li>&mdash; staging, <a href="#Page_177">177</a></li>
+<li>Top booms, <a href="#Page_18">18</a></li>
+<li>Traffic during reconstruction, <a href="#Page_177">177</a></li>
+<li>Transverse bracing, <a href="#Page_34">34</a>, <a href="#Page_117">117</a></li>
+<li>Trough floors, <a href="#Page_27">27</a>, <a href="#Page_180">180</a></li>
+<li>&mdash; girders, <a href="#Page_50">50</a>, <a href="#Page_74">74</a></li>
+<li><span class="lettsymb">T</span> stiffeners, breaks in, <a href="#Page_16">16</a></li>
+<li>Twin girders, <a href="#Page_15">15</a>, <a href="#Page_75">75</a></li>
+<li>Twisting of girders, <a href="#Page_11">11</a>, <a href="#Page_68">68</a>, <a href="#Page_73">73</a></li>
+<li>&mdash; &mdash; &mdash; corrected, <a href="#Page_12">12</a></li>
+<li>Types of reconstruction, <a href="#Page_174">174</a></li>
+<li class="first"><span class="lettsymb">U</span>-shaped booms, <a href="#Page_18">18</a></li>
+<li>Uncomplicated stress, <a href="#Page_62">62</a></li>
+<li>Uniform pressure on bearings, <a href="#Page_6">6</a></li>
+<li class="first">Value of E in deflection formul&aelig;, <a href="#Page_87">87</a></li>
+<li>Vibration, <a href="#Page_162">162</a></li>
+<li class="first">Wasted webs, <a href="#Page_14">14</a>, <a href="#Page_29">29</a>, <a href="#Page_96">96</a></li>
+<li>Water, scour of, <a href="#Page_161">161</a></li>
+<li>Web buckling, <a href="#Page_16">16</a></li>
+<li>&mdash; plates, cracked, <a href="#Page_13">13</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_50">50</a></li>
+<li>&mdash; rivets, <a href="#Page_46">46</a>, <a href="#Page_50">50</a></li>
+<li>&mdash; stiffening, <a href="#Page_16">16</a>, <a href="#Page_38">38</a>, <a href="#Page_185">185</a></li>
+<li>Widening masonry bridges, <a href="#Page_182">182</a></li>
+<li>&mdash; metallic bridges, <a href="#Page_179">179</a></li>
+<li>Wide spaced rivets, <a href="#Page_79">79</a></li>
+<li>Wind pressure, <a href="#Page_41">41</a>, <a href="#Page_43">43</a></li>
+<li class="first">Yielding of piers, <a href="#Page_8">8</a>, <a href="#Page_83">83</a>, <a href="#Page_159">159</a></li>
+</ul>
+
+<hr class="chap" />
+
+<p class="center fsize80">LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,<br />
+GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.</p>
+
+<hr class="chap" />
+
+<div class="tnbox"><a name="TN" id="TN"></a>
+<h2>Transcriber&#8217;s Notes</h2>
+
+<p>The text of the original work (including inconsistent spelling, hyphenation, formatting etc.) has been retained, except as mentioned below.<br />
+The slight differences between the Table of Contents and the text have not been changed</p>
+
+<p><b>Changes made to the text:</b><br />
+Some punctuation errors and obvious typographical errors have been corrected silently.<br />
+Several illustrations have been moved to where they are described in the text.<br />
+Page 123, formula (2): the original shows an unclear superscript after the first L. As described in the following line of the text, this has been changed to L<sub class="lg"><i>l</i></sub>.</p>
+
+</div>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
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+</body>
+</html>
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+Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Anatomy of Bridgework
+
+Author: William Henry Thorpe
+
+Release Date: December 6, 2013 [EBook #44371]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ANATOMY OF BRIDGEWORK ***
+
+
+
+
+Produced by Chris Curnow, Harry Lame and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+
+Transcriber's Notes:
+
+Text between underscores represents _italics_, small capitals have been
+transcribed as ALL CAPITALS.
+
+Curly brackets indicate {subscripts}; letters between square brackets
+(such as [T] and [U]) represent the shape rahter than the letter itself.
+
+More Transcriber's Notes may be found at the end of this text.
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK
+
+  BY
+
+  WILLIAM HENRY THORPE
+  ASSOC. M. INST. C. E.
+
+  WITH 103 ILLUSTRATIONS
+
+  [Illustration]
+
+  London
+  E. & F. N. SPON, LIMITED, 57 HAYMARKET
+  New York
+  SPON & CHAMBERLAIN, 123 LIBERTY STREET
+
+  1906
+
+
+
+
+PREFACE
+
+
+In offering this little book to the reader interested in Bridgework, the
+author desires to express his acknowledgments to the proprietors of
+"Engineering," in which journal the papers first appeared, for their
+courtesy in facilitating the production in book form.
+
+It may possibly happen that the scanning of these pages will induce
+others to observe and collect information extending our knowledge of
+this subject--information which, while familiar to maintenance engineers
+of experience, has not been so readily available as is desirable.
+
+No theory which fails to stand the test of practical working can
+maintain its claims to regard; the study of the behaviour of old work
+has, therefore, a high educational value, and tends to the occasional
+correction of views which might otherwise be complacently retained.
+
+  60 WINSHAM STREET,
+  CLAPHAM COMMON, LONDON, S.W.
+  _October_, 1906.
+
+
+
+
+CONTENTS
+
+
+  CHAPTER I.
+
+  INTRODUCTION--GIRDER BEARINGS.
+
+                                                                    PAGE
+
+  Pressure distribution--Square and skew bearings--Fixed bearings--
+  Knuckles--Rollers--Yield of supports                                 1
+
+
+  CHAPTER II.
+
+  MAIN GIRDERS.
+
+  _Plate webs_: Improper loading of flanges--Twisting of girders--
+  Remedial measures--Cracks in webs--Stiffening of webs--[T]
+  stiffeners                                                           9
+
+  _Open webs_: Common faults--Top booms--Buckling of bottom booms--
+  Counterbracing--Flat members                                        17
+
+
+  CHAPTER III.
+
+  BRIDGE FLOORS.
+
+  Liability to defects--Impact--Ends of cross and longitudinal
+  girders--Awkward riveting--Fixed ends to cross girders--Plated
+  floor--Liberal depths desirable--Type connections--Effect of "skew"
+  on floor--Water-tightness--Drainage--Timber floors--Jack arches--
+  Corrugated sheeting--Ballast--Rail joints--Effect of main girders
+  on floors                                                           20
+
+
+  CHAPTER IV.
+
+  BRACING.
+
+  Effect of bracing on girders--Influence of skew on bracing--Flat
+  bars--Overhead girders--Main girders stiffened from floor--
+  Stiffening of light girders--Incomplete bracing--Tall piers--Sea
+  piers                                                               34
+
+
+  CHAPTER V.
+
+  RIVETED CONNECTIONS.
+
+  Latitude in practice--Laboratory experiments--Care in considering
+  practical instances--Main girder web rivets--Lattice girders
+  investigated--Rivets in small girders--Faulty bridge floor--
+  Stresses in rivets--Cross girder connections--Tension in rivets--
+  Defective rivets--Loose rivets--Table of actual rivet stresses--
+  Bearing pressure--Permissible stresses--Proposed table--Immunity of
+  road bridges from loose rivets--Rivet spacing                       45
+
+
+  CHAPTER VI.
+
+  HIGH STRESS.
+
+  Elastic limit--Care in calculation--Impact--Examples of high stress
+  --Early examples of high stress in steel girders--Tabulated
+  examples--General remarks                                           61
+
+
+  CHAPTER VII.
+
+  DEFORMATIONS.
+
+  Various kinds--Flexing of girder flanges--Examples--Settlement
+  deformations--Creeping--Temperature changes--Local distortions--
+  Imperfect workmanship--Deformation of cast-iron arches              73
+
+
+  CHAPTER VIII.
+
+  DEFLECTIONS.
+
+  Differences as between new work and old--Influence of booms and web
+  structure on deflection--Yield of rivets and stiffness of
+  connections--Working formulae--Set--Effect of floor system--
+  Deflection diagrams--Loads quickly applied--"Drop" loads--Flexible
+  girders--Measuring deflections--New method of observing deflections
+  --Effect of running load                                            85
+
+
+  CHAPTER IX.
+
+  DECAY AND PAINTING.
+
+  Examples of rusting of wrought-iron girders--Girder over sea-water
+  --Rate of rusting--Steelwork--Precautions--Red-lead--Repainting--
+  Scraping--Girders built into masonry--Cast iron--Effect of sea-
+  water on cast iron--Examples--Tabulated observations--Percentage of
+  submersion--Quality of metal                                        96
+
+
+  CHAPTER X.
+
+  EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+  Purpose--Methods of examination--Calculations--Stress in old work--
+  Methods of reducing stress--Repair--Loose rivets--Replacing wasted
+  flange plates--Adding new to old sections--Principles governing
+  additions--Example--Strengthening lattice girder bracings--Bracing
+  between girders--Strengthening floors--Distributing girders        107
+
+
+  CHAPTER XI.
+
+  STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+  Principal methods in use--Method of calculation--Adjustments--
+  Connections--Method of execution--Checks--Effect of skew on method
+  considered--Results of calculation for a typical case--Probable
+  error--Practical examples--Special case--Method of determining
+  flexure curves                                                     122
+
+
+  CHAPTER XII.
+
+  CAST-IRON BRIDGES.
+
+  Limitations of cast iron--Stress examples--Advantages and
+  disadvantages--Foundry stresses--Examples--Want of ductility of
+  cast iron--Repairs--Restricted possibilities                       141
+
+
+  CHAPTER XIII.
+
+  TIMBER BRIDGES.
+
+  Perishable nature--Causes of decay--Sag--Lateral bracing--Piles--
+  Uncertainty respecting decay--Examples--Conditions and practice
+  favourable to durability--Bracing--Protection--Repair--Piles--Cost 149
+
+
+  CHAPTER XIV.
+
+  MASONRY BRIDGES.
+
+  Definition--Cause of defects or failure--Spreading of abutments--
+  Closing in--Example--Stop piers--Example of failure--Strength of
+  rubble arch--Equilibrium of arches--Effect of vibration on masonry
+  --Safety centring--Methods of repair--Pointing--Rough dressed
+  stonework                                                          157
+
+
+  CHAPTER XV.
+
+  LIFE OF BRIDGES--RELATIVE MERITS.
+
+  Previous history--Causes of limited life--Tabulated examples of
+  short-lived metallic bridges--Timber and masonry bridges--
+  Durability--Maintenance charges--First cost--Comparative merits--
+  Choice of material                                                 165
+
+
+  CHAPTER XVI.
+
+  RECONSTRUCTION AND WIDENING OF BRIDGES.
+
+  CONCLUSION.
+
+  Measuring up--Railway under-bridges--Methods of reconstruction in
+  common use--Reconstruction of bridges of many openings--Timber
+  staging--Traffic arrangements--Sunday work--Railway over-bridges--
+  Widenings--Junction of new and old work--Concluding remarks--Study
+  of old bridgework                                                  172
+
+  INDEX                                                              187
+
+
+
+
+  THE
+  ANATOMY OF BRIDGEWORK.
+
+
+
+
+CHAPTER I.
+
+INTRODUCTION.
+
+
+No book has, so far as the author is aware, been written upon that
+aspect of bridgework to be treated in the following pages. No excuse
+need, therefore, be given for adding to the already large amount of
+published matter dealing with bridges. Indeed, as it too often happens
+that the designing of such constructions, and their after-maintenance,
+are in this country entirely separated, it cannot but be useful to give
+such results of the behaviour of bridges, whether new or old, as have
+come under observation.
+
+In the early days of metallic bridges there was of necessity no
+experience available to guide the engineer in his endeavour to avoid
+objectionable features in design, and he was, as a result, compelled to
+rely upon his own foresight and judgment in any attempt to anticipate
+the effects of those influences to which his work might later be
+subject. How heavily handicapped he must have been under these
+conditions is evident from the mass of information since acquired by the
+experimental study of the behaviour of metals under stress, and the
+growth of the literature of bridgework during the last forty years. That
+many mistakes were made is little occasion for surprise; rather is it a
+cause for admiration that some very fine bridges, still in use, were
+the product of that time. Much may be learned from the study of defects
+and failures, even though they be of such a character that no
+experienced designer would now furnish like examples.
+
+Modern instances may, none the less, be found, with faults repeated,
+which should long since have disappeared from all bridgework, and are
+only to be accounted for by the unnatural divorce of design and
+maintenance already referred to. As the reader proceeds, it may appear
+that details are occasionally touched upon of a character altogether too
+crude and objectionable to need comment; but the consideration of these
+cases is none the less interesting, and, so far as the author's
+observation goes, not altogether unnecessary.
+
+Most of the instances cited are of bridges, or parts of bridges, of
+quite small dimensions; but it is these which most commonly give
+trouble, both because the effects of impact are in such cases most
+severely felt, and possibly because the smaller class of bridges is very
+generally designed by men of less experience, than large and imposing
+structures.
+
+The particulars given relate in all cases to bridges of wrought iron,
+unless otherwise described.
+
+An endeavour has been made to secure some kind of order in dealing with
+the subject, but it has been found difficult to avoid a somewhat
+disjointed treatment, inseparable, perhaps, from the nature of the
+matter. Finally, the reader may be assured that every case quoted has
+come under the writer's personal notice.
+
+
+GIRDER BEARINGS.
+
+In girder-work generally, and more particularly in plate-girders,
+considerable latitude obtains in the amount of bearing allowed. Clearly,
+the surface over which the pressure is distributed should be
+sufficiently ample to avoid overloading and possible crushing or
+fracture of bedstones where these exist; but if no knuckles are
+introduced, this is an extremely difficult matter to insure. A long
+bearing may deliver the load at the extreme end of the surface on which
+it rests, or, more probably, near the face.
+
+If the girder is made with truly level bearings, and the beds set level,
+it will certainly, when under load, throw an extreme pressure upon that
+part of the bearing surface immediately under the forward edge of the
+bearing-plate. These considerations probably account for bedstones
+frequently cracking, in addition to which possibility there is the
+disadvantage that the designer does not know where the girder will rest,
+and cannot truly define the span. The variation of flange-stress due to
+this cause may, in a girder of ordinary proportions, having bearings
+equal in length to the girder's depth, be as much as 15 per cent. above
+or below that intended.
+
+If great care be taken in setting beds, in the first instance, to dip
+toward the centre of the span an amount depending upon the anticipated
+girder deflection, it may be possible to insure that when under full
+load the girder bearing shall rest equally upon its seat; but this is
+evidently a difficult condition to obtain practically, is good only for
+one degree of loading, and may at any time be nullified by a disturbance
+of the supports, as, for instance, the very common occurrence of a
+slight leaning forward of abutment walls.
+
+Double or treble thicknesses of hair-felt are sometimes placed beneath
+girder bearings, with the object of securing a better distribution of
+pressure, no doubt with advantage; but this practice, though it may be
+quite satisfactory as applied to girders carrying an unchangeable load,
+hardly meets the case for loads which are variable. Notwithstanding the
+faulty nature of the plain bearing ordinarily used for girders of
+moderate span, its extreme simplicity commends it to most engineers. It
+must be admitted that no serious inconvenience need be anticipated in
+the majority of cases, particularly if the bearings are limited in
+length, do not approach nearer than 3 inches to the face of bedstones,
+and are furnished with hair-felt or similar packing.
+
+[Illustration: FIG. 1.]
+
+Whether with long or short bearings, the forward edge should be at right
+angles to the girder's length. In skew bridges it is sometimes seen that
+this edge follows the angle of skew. The effect on the girder is to
+twist it, as will be clear from a little consideration. In evidence of
+this the case may be quoted of a lattice girder of 95 feet effective
+span and 7 feet deep, which, resting on a skew abutment right up to the
+masonry face at a rather bad angle (about 15 degrees), was, after twenty
+years, found canted over at the top to the extent of 4 inches, with the
+further result of springing a joint in the top flange at about the
+middle of the girder, causing some rivets to loosen. The bedstone was
+also very badly broken at the face, and had to be replaced in the course
+of repairs (Fig. 1). This girder had, in addition to the canting from
+the upright position at its end, and the distortion of the top flange, a
+curvature in the same direction, though less in amount, at the
+bottom--an effect very common in the main girders of skew bridges, and
+possibly accounted for in part by a tendency of the girder end to creep
+along the abutment away from the point at which it bears hardest, under
+frequent applications and removals of the live load, and accompanying
+deflections.
+
+This tendency to travel may be aggravated in bridges carrying a
+ballasted road, in which there may be a considerable thickness of
+ballast near the bearings, by the compacting and spreading of this
+material taking effect upon the girder end, tending to push it outwards,
+being tied only by a few light cross-girders badly placed for useful
+effect. The movement may be prevented in new work for moderate angles of
+skew by carrying the end cross-girders well back, and securing them in
+some efficient manner; or by the introduction of a diagonal tie
+following the skew face, and attached to cross and main girder flanges
+(Fig. 2)--a method which may be applied to existing work also.
+
+[Illustration: FIG. 2.]
+
+For such a case as that cited it is imperative that ballast pressure at
+the girder end should be altogether eliminated.
+
+The fixing of girder ends by bolts--a practice at one time usual--hardly
+calls for remark, as it is now seldom resorted to unless for special
+reasons; but it may be well to point out the weakening effect of holes
+for any purpose in bedstones. Bed-plates commonly need no fixing; the
+weight carried keeps them in position, or if, in the case of very light
+girders upon separate plates, it is considered well to secure these from
+shifting, it may best be done by letting the plate in bodily a small
+amount, or by means of a very shallow feather sunk into a chase.
+
+[Illustration: FIG. 3.]
+
+As an improvement upon the plain bearing usually adopted, it is an easy
+matter so to design girder-ends as to deliver the load by a narrow strip
+of bearing-plate carried across the bottom flange, distributing the
+pressure upon the stone, if there be one, by means of a simple
+rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle
+will by this means result, with freedom to slide, and the girder span be
+defined within narrow limits. A true knuckle is, of course, the best
+means of securing imposition of the load always in the same place; but
+this by itself is not sufficient where the girder is of a length to make
+temperature and stress variations important, in which case rollers, or
+freedom to slide, become necessary. Bridges exist in which
+roller-bearings have been adopted without the knuckle, or its
+equivalent, but this is wholly indefensible, as it is obvious that the
+forward roller will in all probability take the whole load, and cannot
+be expected to keep its shape and roll freely under this mal-treatment.
+It is sometimes asserted that rollers are never effective after some
+years' use; that they become clogged with dirt, and refuse to perform
+their office.
+
+There is no reason why rollers should not be boxed in to exclude dirt by
+a casing easily removed, some attention being given to them, and any
+possible accumulation of dirt removed each time the bridge is painted.
+
+To test the behaviour of rollers under somewhat unfavourable conditions
+for their proper action--that of the bearings of main roof trusses of
+crescent form, 190 feet span--the author, some thirty years since, took
+occasion to make the necessary observations, and found evidence of a
+moderate roller movement, though there was in this case no direct
+horizontal member to communicate motion. With girders resting upon
+columns, particularly if of cast iron, a roller and knuckle arrangement
+is most desirable for any but very small spans, as, if not adopted, the
+result will be a canting of the columns from side to side--a very small
+amount, it is true, but sufficient to throw the load upon the extreme
+edges of the base, though the knuckle alone will relieve the top of this
+danger. The author at one time took the trouble to examine, so far as it
+could be done superficially and without opening out the ground to make a
+complete inspection possible, a number of bridges crossing streets, in
+which girders rested upon and were secured to cast-iron columns standing
+in the line of kerb; and he found cracks, either at the top or bottom,
+in about one of every four columns.
+
+When girders passing over columns are not continuous, it may be
+difficult to find room for a double roller and knuckle arrangement; but
+this inconvenience may be overcome by carrying one girder-end wholly
+across the column-top, and securing the next girder-end to it in a
+manner which a little care and ingenuity will render satisfactory, one
+free bearing then serving to carry the load from both girders.
+
+Though the wisdom of using rollers is apparent in spans exceeding some
+moderate length, say 80 feet--as to which engineers do not seem quite
+decided--and varying with the conditions, it need not be overlooked that
+in some cases masonry will be sufficiently accommodating to render them
+unnecessary; piers, if sufficiently tall and slender, will yield a small
+amount without injury, and though shorter, if resting upon a bottom not
+absolutely rigid, will rock and give the necessary relief; but it is
+obvious, if the resistance to movement is sufficiently great, and the
+girder cannot slide or roll on its bearings, bedstones will probably
+loosen, as, indeed, frequently happens.
+
+
+
+
+CHAPTER II.
+
+MAIN GIRDERS; PLATE-WEBS.
+
+
+It is seldom that girders of this description--or, indeed, of any
+other--show signs of failure from mere defect of strength in the
+principal parts, even though somewhat highly stressed; and instances
+tending to support this statement will be given in a later chapter. For
+the present, it is proposed to indicate peculiarities of behaviour only,
+generally, but not always, harmless.
+
+Though now less often done, it was at one time common practice to load
+plate-girders on the bottom flange by simply resting floor timbers,
+rails, troughs, or cross-girders upon them. In outside girders one
+result of this is to cause the top flange to take a curve in plan,
+convex towards the road, every time the live load comes upon the floor
+of the bridge, upon the passing of which the flange resumes its figure,
+though still affected by that part of the load which is constant.
+
+A bridge of 47 feet span, carrying two lines of way, having one centre
+and two outside girders, with a floor consisting of old Barlow rails,
+resting upon the bottom flanges, showed the peculiarity named in a
+marked degree.
+
+The outside girders, under dead load only, were, as to the top flanges
+(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of
+straight in their length, but upon the passing of a goods engine and
+train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one
+outside girder, and 2-3/16 inches for the other.
+
+The centre girder, having a broader and heavier top flange, curved 5/8
+inch towards whichever road might be loaded. The effect of such
+horizontal flexure is clearly to induce stresses of tension and
+compression in the flanges, which, being (for the top flange) compounded
+with the normal compressive stress due to load carried, results in a
+considerable want of uniformity across the section.
+
+[Illustration: FIG. 4.]
+
+In the case under notice, the writer estimates the stresses for an outer
+girder top flange at 4.5 tons per square inch compression for simple
+loading, and 5.5 tons per square inch of tension and compression, on the
+inner and outer edges, due to flexure, resulting when compounded in a
+stress of 1 ton per square inch tension on the inside, and 10 tons per
+square inch compression on the outside edge. In this rather extreme case
+the stress on the inner edge, or that nearest the load, is reversed in
+character.
+
+The effect described appears to be not wholly due to the twisting
+moment. It is apparent that whatever curvature may be induced by
+twisting alone must be aggravated in the compression flange by its being
+put out of line.
+
+The writer does not attempt here to apportion the two effects in any
+other way than to say that the greater part of the flexure appears to be
+due to the secondary cause. Consistent with this view of the matter is
+the fact that the inclination of the girder towards the rails greatly
+exceeded the calculated slope of the Barlow rail-ends when under load,
+being about five times as great. The inference is that the floor rails
+bore hard at their extreme ends, at which point of bearing the
+calculated twisting moment accounts for less than one-half of the
+flexure observed in the flanges.
+
+[Illustration: FIG. 5.]
+
+The girders upon removal in the course of reconstruction again took the
+straight form, showing that the very frequent development of the
+stresses named had not sensibly injured the metal, though the bridge
+carried as many as three hundred trains daily in each direction, and had
+done so for very many years.
+
+The deformation of the top flange only has been noticed, yet the same
+tendency exists in the bottom, though the actual amount is much less,
+both because the lower flanges are in tension, and are also in great
+degree confined by the frictional contact of the cross bearers, even
+where no proper ties are used. In the case dealt with the bottom flanges
+of the outer girders curved 1/8 inch outwards only.
+
+With the broad flanges commonly adopted in English practice, twisting of
+the girders, under conditions similar to the above, will not generally
+be a serious matter; but with narrow flanges possessing little lateral
+stiffness it might be a source of danger.
+
+[Illustration: FIG. 6. FIG. 7.]
+
+The twisting may be limited in amount by introducing a cross-frame
+between the girders, from which they are stiffened; by strutting the
+girders immediately from the floor itself, in which case they cannot
+cant to a greater extent than that which corresponds to the floor
+deflection; or by designing the top flange to be unsymmetrical with
+reference to the web, as in Figs. 6 and 7, with the object of insuring
+that under the joint effect of vertical loading and twisting, the stress
+in the flange shall at maximum loads be uniform across the section, and
+allow it to remain straight. This may be secured by making the
+eccentricity of the flange section equal to that of the loading. For
+instance, if the load be applied 3 inches away from the web centre, the
+flange should have its centre of gravity 3 inches on the other side of
+the centre line. It can be shown that this is true throughout the length
+of the girder, and irrespective of the depth. An instance in which
+flange eccentricity being in excess, curvature outwards resulted, will
+be found in a later chapter on deformations, etc. It will not generally
+be necessary to make the bottom flange eccentric, as it is commonly tied
+in some way; but if done, the eccentricity should be on the same side as
+for the top. The flanges remaining straight under these conditions are
+not subject to the complications of stress referred to in the case first
+quoted. The author has adopted both the last named details in bridges
+where he has been obliged to accept unfair loading of the kind
+discussed.
+
+It should be remarked that by the two first methods, if the stiffening
+frames are wide apart and attached direct to the web, there is a
+liability for this to tear, under distress, rather than keep the girder
+in line.
+
+There is one other possible consequence of throwing load upon the
+flanges of a girder of a much more alarming nature. In girders not very
+well stiffened, it may happen that the frequent application of load in
+this manner finally so injures the web-plate, just above the top edge of
+the bottom angle-bars, as to cause it to rip in a horizontal direction.
+More likely is this to happen with a centre girder taking load first on
+one side, then on the other, and again on both together. Cases may be
+cited in which cracks right through the webs 3 feet or more in length
+have resulted from this cause. It is very probable, however, that in
+some of these cases the matter was aggravated by the use of a poor iron
+in the webs, as at one time engineers, from mistaken notions of the
+extreme tenuity permissible in webs near the centre of a girder, would,
+if they could not be made thin enough, even encourage the use of an
+indifferent metal as being quite good enough for that part of the work.
+
+An instance of web-fracture from somewhat similar causes may be here
+given.
+
+In a bridge of 31 feet 6 inches effective span, and consisting of twin
+girders carrying rails between, as shown in Figs. 8 and 9, the load
+resting upon the inner ledges, formed by the bottom flange, induced
+such a bending and tearing action along the web just above the
+angle-bars, as to cause a rip in one of the girders, well open for some
+distance, and which could be traced for 14 feet as a continuous crack.
+
+[Illustration: FIG. 8.]
+
+[Illustration: FIG. 9.]
+
+It will be noticed in the figure that the [T] stiffeners occur only at
+the outer face of the web, and that the inner vertical strips stop short
+at the top edge of the angles, the result being that under load the
+flange would tend to twist around some point, say A, at each stiffener,
+inducing a serious stress in the thin web at that place, while away from
+these stiffeners the web would be more free to yield without tearing.
+The fact that at a number of the stiffeners incipient cracks were
+observed, some only a few inches long, suggests this view of the matter.
+
+A case of web-failure from other influences coming under notice showed
+breaks at the upper part of the web extending downwards.
+
+In this bridge, of 32 feet span, which had been in existence thirty-two
+years, the webs--originally 1/4 inch thick--were, largely because of
+cinder ballast in contact with them, so badly wasted as to be generally
+little thicker than a crown-piece, and in places were eaten through; in
+addition to which, the road being on a sharp curve, the rail-balks had
+been strutted from the webs to keep them in position, the effect of
+which would be to exert a hammering thrust upon the face of the web at
+the abutting ends, and assist in starting cracks in webs already much
+corroded. A feature of this case, tending to show that the breaks
+resulted as the joint effect of waste and ill-usage by the strut
+members, rather than by excessive stress in the web as reduced, is to be
+found in the fact that the girders when removed were observed to be in
+remarkably good shape--i.e. the camber, marked on the original drawings
+to be 1-1/2 inch, still showed as a perfectly even curve of that rise,
+which would hardly have been the case if the lower flange had been let
+down by web-rupture, the result of excessive web-stresses.
+
+Occasionally webs will crack through the solid unwasted plate, in a line
+nearly vertical; not where shear stress is greatest, but generally at
+some other place, and from no apparent cause, either of stress or
+ill-usage. The writer has observed this only in the case of small
+girders not exceeding 2 feet in depth; and, for want of any better
+reason, attributes these cracks to poor material, coupled with some
+latent defect. In a bridge having some thirty cross-girders, each 26
+feet long, about every other one had a web cracked in this manner after
+many years' use.
+
+Web-cracks of the kind first indicated, are perhaps, the most probable
+source of danger in plate-girders, of any which are likely to occur. The
+fault is insidious, difficult to detect when first developed, and
+perhaps not seen at all till the bridge, condemned for some other
+reason, has the girders freely exposed and brought into broad light. The
+manner in which old girders are sometimes partly concealed by
+timberwork, or covered by ballast, makes the detection of these defects
+an uncertain matter, unless sufficient trouble is occasionally taken to
+render inspection complete.
+
+The manner in which girders with wasted and fractured webs will still
+hang together under heavy loading seems to warrant the deduction that,
+in designing new work, it can hardly be necessary to provide such a
+considerable amount of web-stiffening as is sometimes seen; experience
+showing that defects of the web-structure do not commonly occur in the
+stiffening so frequently as in the plate, and then in the form of
+cracks.
+
+A case of web-buckling lies, so far, without the author's experience.
+There is no need to introduce, for web-stresses alone, more stiffening
+than that which corresponds to making the stiffeners do duty as vertical
+struts in an openwork girder; in which case it is sufficient to insure
+that the stiffeners occurring in a length equal to the girder's depth
+shall, as struts, be strong enough in the aggregate to take the whole
+shear force at the section considered, in no case exceeding this amount
+on one stiffener. For thin webs in which the free breadth is greater
+than one hundred and twenty times the thickness, the diagonal
+compressive stress may be completely ignored, and the thickness
+determined with reference to the diagonal tension stress only.
+
+There is one fault which frequently shows itself in stiffeners though
+not the result of web-stresses, and when performing an additional
+function--viz., the breaking of [T] stiffener knees at the weld, where
+brought down on to the tops of cross-girders, due to the deflection of
+the floor, as shown in Fig. 10. When such knees are used, the angle may
+properly be filled in with a gusset-plate to relieve the weld of strain
+and prevent fracture.
+
+[Illustration: FIG. 10.]
+
+There is some little temptation in practice to make use of the solid web
+as a convenient stop for ballast, or road material. Special means,
+perhaps at the cost of some little trouble, should be adopted, where
+necessary, to avoid this.
+
+
+MAIN GIRDERS; OPEN WEBS.
+
+With these, as with plate-girders, deficiency of strength--i.e. of
+section strength--is seldom so marked as to be a reasonable cause of
+anxiety. In particular instances faults in design may result in stresses
+of an abnormal amount, though rarely to an extent occasioning any ill
+effects. The practice of loading the bottom flanges at a distance from
+the centre, the bad effects of which have already been dealt with as
+applied to plate-girders, is not commonly resorted to in girders having
+open webs, nor are these so liable to be heaped with ballast in
+immediate proximity to essential members of the structure.
+
+Some defects are, however, occasionally seen which may be remarked. Top
+booms of an inverted [U] section are sometimes made with side webs too
+thin, and having the lower edges stiffened insufficiently, or not at
+all. Where this is the case, the plates may be seen to have buckled out
+of truth, showing that they are unable, as thin plates, to sustain the
+compressive stress to which the rest of the boom is liable. The practice
+of putting the greater part of the boom section in an outer flange,
+characteristic of this defect, has the further disadvantage of throwing
+the centre of gravity of the section so near its outer edge as to make
+impracticable the best arrangement of rivets for connection of the web
+members. Further, since all the variation in boom section is thrown into
+the flange-plates, the centre of gravity of the section has no constant
+position along the boom--an additional inconvenience where correct
+design is aimed at.
+
+These considerations indicate the propriety of arranging the bulk, or
+all, of the section at the sides, thus reducing or getting rid of the
+objections named.
+
+Where the bottom boom consists of side plates, only one point demands
+attention. It is found that, though nominally in tension, the end bays
+are liable occasionally to buckle, as though under compressive stress,
+and need stiffening, not excepting girders which at one end are mounted
+on rollers. This might seem to indicate that the rollers are of no use;
+but it is conceivable the resistance arises from other causes, such as
+wind forces, or as in the case of a bridge carrying a railway, in which
+the rigidity of the permanent-way may be such that the bridge-structure,
+in extending towards the roller end, cannot move it sufficiently,
+causing a reversal of stress on the lighter portions of the bottom boom
+at the knuckle end; or by the exposed girder booms becoming very
+sensibly hotter than the bridge floor, and by expanding at a greater
+rate, cause this effect, from which rollers cannot protect them.
+
+In counterbracing consisting of flat bars it is desirable either to
+secure these where they cross other members, or stiffen them in some
+manner to avoid the disagreeable chattering which will otherwise
+commonly be found to occur on the passage of the live load.
+
+Occasionally diagonal ties are made up of two flat bars placed face to
+face, to escape the use of one very thick member. Where this is done,
+the two thicknesses, if not riveted together along the edges, will be
+liable to open, as the result of rusting between the bars in contact,
+when the evil will be aggravated by the greater freedom with which
+moisture will enter the space.
+
+Other matters relating to open-web girders will be more conveniently
+dealt with under their separate headings, particularly a further
+consideration of the relationship subsisting between the booms and floor
+structure.
+
+
+
+
+CHAPTER III.
+
+BRIDGE FLOORS.
+
+
+The floors of bridges commonly give more trouble in maintenance, and
+their defects are more frequently the cause which renders reconstruction
+necessary, apart from reasons not concerning strength, than any other
+part of such structures. When it is considered that this portion of a
+bridge is first affected by impact of the load which comes upon it, and
+is usually light in comparison with the main girders further removed
+from the load, and to which the latter is transferred through the more
+or less elastic floor, the fact will be readily appreciated by those not
+already familiar with it.
+
+The end attachments of cross and longitudinal girders are very liable to
+suffer by loosening of rivets, or, more rarely, by breaking of the
+angle-irons which commonly make such a connection. A not unusual defect
+of old work, which may also sometimes be seen in work quite new, where
+the cross-girder depth has from any cause been restricted, is the
+extremely cramped position of the rivets securing the ends. There is
+small chance of these ever being properly tight, if the act of riveting
+is rendered difficult by bad design. This is the more objectionable if
+it happens that cross-girder ends abut against opposite sides of the web
+of an intermediate main girder, and are secured by the same rivets
+passing through. At the best such rivets will not be well placed to
+insure good workmanship, and the severe treatment to which they become
+subject, as the cross-girders take their load and deflect under it,
+will be very apt to loosen them. The author has seen a case of this kind
+(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the
+whole of the cross-girder end rivets were loose, some nearly worn
+through, thus allowing the cross-girders to be carried, not by their
+attachments, but by resting upon the main-girder flanges, which in turn,
+by repeated twisting, tore the web for a length of 4 feet; there was
+also pronounced side flexure of the top booms. The movements generally
+on this bridge (of 42-feet span), whether of main or cross-girders, were
+very considerable and disturbing. It was removed after about
+twenty-three years' use.
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+There is no necessity, as a rule, for the ends of cross-girders attached
+to the same main girder at opposite sides to be placed in line. The
+author prefers to arrange them to miss, by which device each connection
+is entirely separate, the riveting can be more efficiently executed,
+erection is simplified, and the rivets will be more likely to keep
+tight. Other special cases of cross-girder ends will be dealt with under
+the head "Riveted Connections."
+
+It is sometimes contended that cross-girders attached at their ends by a
+riveted connection should be designed as for fixed ends, in which case
+they are usually made of the same flange section throughout, with a view
+to satisfy the supposed requirements. But a girder to be rightly
+considered as having fixed ends must be secured to something itself
+unyielding. With an outer main girder of ordinary construction, and no
+overhead bracing, this is so far from being the case as to leave little
+occasion for taking the precaution named. As the cross-girders deflect,
+the main girders will commonly yield slightly, inclining bodily towards
+the cross-girders, if these are attached to the lower part of the main
+girders. The force requisite to cant the main girders in this manner is
+usually less than that which corresponds to fixing the cross-girder
+ends, and is, generally, slight. It is, of course, necessary that this
+measure of resistance at the connection should be borne in mind for the
+sake of the joint itself, quite apart from any question of fixing.
+
+Possibly, in quite exceptional cases, where very stiff main girders are
+braced in such a manner as to prevent canting, it may be proper to
+consider the cross-girder ends as fixed, or for those near the bearings
+of heavy main girders; but the author has not met with any example where
+cross-girders, apart from attachments, appear to have suffered from
+neglect of this consideration.
+
+With cross-girders placed on either side of a main girder, and in line,
+it may also, for new work, be desirable to regard the ends as fixed, and
+to detail them with this in view. It does not, however, appear wise to
+carry this assumption to its logical issue, and reduce the flange
+section to any appreciable extent on this account. The fixity of the
+ends will, in any such case, be imperfect; and when one side only of an
+intermediate main girder is loaded, it can have but a moderate effect in
+reducing flange stress at the middle of the loaded floor beam.
+
+[Illustration: FIG. 13. FIG. 14. FIG. 15.]
+
+Similar reasons affect the design of longitudinal girder attachments to
+cross-girders, which, if intended to support rails, cannot of necessity
+be schemed to come other than in line. Where the floor is plated as one
+plane surface, there will not usually be any trouble resulting if no
+special precautions are used, as the plate itself will insure that the
+longitudinals act, in a measure, as continuous beams, relieving the
+joints of abnormal stress. If the plating is, however, designed in a
+manner which does not present this advantage, or if the floor be of
+timber, it is better to decide whether the connections shall be
+considered as fixed, and made so; or avowedly flexible, and detailed in
+such a manner as to possess a capacity for yielding slightly without
+injury. Those connections are most likely to suffer which are neither of
+the one character nor the other, offering resistance without the ability
+to maintain it. Figs. 13, 14, and 15 give representations of three
+"spring joint" methods of insuring yield in a greater or less degree.
+For small longitudinals it is, perhaps, sufficient to use end angles
+with very broad flanges against the cross-girder web; these to be
+riveted in the manner indicated in Fig. 15.
+
+Liberal depth to floor beams is distinctly advantageous where it can be
+secured, rendering it easier to design the ends in a suitable manner, by
+giving room near mid-depth of the attachment to get in the necessary
+number of rivets; or where the ends are rigidly attached direct to
+vertical members of an open-work truss, the greater depth is effective
+in reducing the inclination of the end from the vertical, with a
+correspondingly reduced cant of the main girders and flexure of the
+vertical member, with smaller consequent secondary stresses. In any case
+deep girders will contribute to stiffness of the floor itself,
+favourable in railway bridges to the maintenance of permanent-way in
+good order.
+
+[Illustration: FIGS. 16, 17, 18.]
+
+A point in connection with skew-bridge floors occasionally overlooked is
+the combined effect of the skew, and main girder camber, in throwing the
+floor structure out of truth, if no regard has been paid to this. The
+result is bad cross-girder or other connections; or, in the case of
+bearers running over the tops of main girders, a necessity for special
+packings to bring all fair (Fig. 17). The author has in such cases,
+where cross-girders are used, set the main girder beds at suitable
+levels, in order that the cross-bearers may all be horizontal (see Figs.
+16 and 18). This may not always be permissible; but, however the
+difficulty may be met, it should be dealt with as part of the design.
+For small angles of skew only may it be neglected.
+
+Rivets attaching cross-girder angles to the web will occasionally
+loosen, probably due in most cases to bad work, together with some
+circumstance of aggravation, as in the case of a bridge floor consisting
+of girders spaced 3 feet 6 inches apart, with short timber bearers
+between, carrying rails. In many girders the top row of rivets, of
+ordinary pitch and size, had loosened, allowing the web, about 1/4 inch
+thick, a movement of 1/8 inch vertically. The rails being very close
+down upon the cross-girder tops, though not intended to touch, had at
+some time probably done so, and by "hammering" produced the result
+described.
+
+Plated floors are often found which are objectionable on account of
+their inability to hold water, arising sometimes from bad work, as often
+from wide spacing of rivets. With rivets arranged to be easily got at,
+and pitched not more than 3 inches apart, a tight floor may be expected;
+but it is still necessary to drain the floor by a sufficient number of
+holes, provided with nozzles projecting below the underside of the
+plate, and sufficiently long to deliver direct into gutters, where these
+are necessary. Drain-holes should not be less frequent than one to every
+50 square feet of floor, if flat, and may advantageously be more so.
+Gutters should slope well, and care be taken to insure practicable
+joints and good methods of attachment--a matter too often left to take
+care of itself, with considerable after-annoyance as a result.
+
+The use of asphalt, or asphalt concrete, to render a plated floor
+water-tight is hardly to be relied upon for railway bridges, though no
+doubt effective for those carrying roads. It is extremely difficult to
+insure that it shall stand the jarring and disturbance to which it may
+be subject, and under which it will commonly break up, and make matters
+worse by holding moisture, and delaying the natural drying of the floor.
+In bulk, as in troughs, it may be useful, but in thin coverings on
+plates it cannot be depended upon.
+
+Floors having plated tops are sometimes finished over abutments or piers
+in a manner which is not satisfactory, either as regards the carrying of
+loads or accessibility for painting. If the plates are carried on to a
+dwarf wall with the intention that the free margin of the plate shall
+rest upon it, there will be a difficulty in securing this in an
+efficient manner. Commonly such a wall is built up after the girder work
+is in place, making it difficult to insure that the wall really supports
+the plate, the result being that this may have to carry itself as best
+it can. In any case, severe corrosion will occur on the underside, and
+the plate rust through much before the rest of the floor; the masonry
+also will usually be disturbed.
+
+It appears preferable to form the end of the floor with a vertical
+skirting-plate having an angle or angles along the lower edge. This may
+come down to a dwarf wall, but preferably not to touch it, the skirting
+being designed to act as a carrying girder. A convenient arrangement is
+shown in Fig. 19, which may be used either for a square or skew bridge.
+It will be seen that the plate-girders have no end-plates, the skirting
+referred to being carried continuously along the floor edge, and
+attached to each girder-web, the whole of the more important parts being
+open to the painter.
+
+[Illustration: FIG. 19.]
+
+Trough floors consisting of one or other of the forms of pressed or
+rolled section present the objection that it is almost impracticable to
+arrange an efficient connection at the ends, if they abut against main
+girders, and but little connection is, as a rule, attempted, and
+sometimes none. The result is that the load from these troughs is
+delivered in an objectionable manner, and the ends being open or
+imperfectly closed, water and dirt escape on to the flange, or other
+ledge, which supports them. A description of pressed floor which
+promises to overcome this objection, and provide a ready means of
+attachment to the webs of plate-girders, or of booms having vertical
+plate-webs, has within the last few years been introduced. This has the
+ends shaped in such a manner as to close them and provide a flat surface
+of sufficient area for connection by rivets. Each hollow is separately
+drained by holes with nozzles. Whether this type of trough will develop
+faults of its own, due to over-straining of the metal in the act of
+pressing, remains to be seen; but as it appears possible to produce the
+desired form without any material thinning or thickening of the metal,
+the contention that no severe usage accompanies the process appears to
+be reasonable.
+
+That form of troughing in which the top and bottom portions are
+separately formed, and connected by a horizontal seam of rivets at
+mid-depth, is found in use upon railway bridges to be very liable to
+loosening of those rivets near the ends; less surprising, perhaps,
+because the sloping sides are usually thin.
+
+It is a distinctly difficult matter to join two or more lengths of any
+trough flooring having sloping sides, in a workmanlike manner; the fit
+of covers is apt to be imperfect, and some rivets, being difficult of
+access, are likely to be but indifferently tight, so that if the joint
+occurs where it will be more than lightly stressed, trouble will
+probably follow. A bad place for such joints is immediately over girders
+supporting the troughs, as there the stress will be most severe, any
+leakage come directly upon the girder, and remedial measures be more
+difficult to carry out.
+
+Timber floors of the best timber, close jointed, are more durable than
+might be supposed. The disadvantage is a difficulty in ascertaining the
+precise condition of the timber after many years' use. The author has
+seen timbers, 9 inches by 9 inches, forming in one length a close floor,
+carried by three girders, and supporting two lines of way, which, when
+taken out, could as to a considerable part be kicked to pieces with the
+foot; whilst in another case, with the same arrangement of girders and
+close-timbered floor, the wood, after being in place for thirty-two
+years, was, when taken out, found to be perfectly sound, with the
+exception of a very few bad places of no great extent. In this instance,
+however, it is known that the floor--pitch-pine--was put in by a
+contractor who prided himself upon the quality of the timber that he
+used; the floor being also covered with tar concrete, which had in this
+instance so well performed its office as to keep the timber quite dry on
+the top.
+
+Jack arches between girders make an excellent floor for road bridges,
+though heavy; and for small bridges may be used to carry rails, if the
+girders are designed to be stiff under load. The apprehension that
+brickwork or concrete will separate from the girder-work, or become
+broken up under even moderate vibration, does not seem to be well
+founded, if the deflection is small and the brickwork or concrete good.
+
+The use of corrugated sheeting as a means of rendering the underside of
+a bridge drop dry cannot be too strongly deprecated. If it must be
+adopted, the arrangement should be such as to permit ready removal for
+inspection and painting. It is evident that by boxing up the floor
+structure, rust is favoured, and serious defects may be developed, not
+to be discovered till the sheeting is removed, or something happens.
+
+[Illustration: FIG. 20.]
+
+A case may be instanced in which it was found, on taking down sheeting
+of this description, that the floor girders, previously hidden, were
+badly wasted in the webs. One of these girders had cracked, as shown in
+Fig. 20, and others were in a condition only less bad.
+
+In any floor carrying ballast or macadam, if means are not adopted to
+keep the road material from the structure of the floor, or from the main
+girders, corrosion may be serious in its effects. Cinder ballast is,
+perhaps, the worst in this respect, in its action upon steel or
+ironwork, being distinctly more damaging than any other kind commonly
+used.
+
+Rail-joints upon bridge floors are to be avoided where practicable by
+the use of rails as long as can be obtained; if the bridge is small
+enough, crossing it in one length. At each joint there is likely to be
+hammering and working extremely detrimental to floor members and
+connections; indeed, it may happen that loose rivets will be found in
+the neighbourhood of such joints, and nowhere else on the bridge. Where
+rail-joints cannot be avoided, their position should, if there be any
+choice, be judiciously selected, and the plate-layers taught to close
+the joints and jam the fish-bolts.
+
+[Illustration: FIG. 21.]
+
+As rail-joints upon a bridge may injuriously affect the floor, so also
+will a weak floor be very trying to the rails. A remarkable instance of
+this has come under the writer's notice, where a bridge (Fig. 21) of
+three 33-feet spans, having outer and centre main girders, with
+cross-girders spaced 3 feet apart, resting upon the girder flanges, but
+not attached, and carrying two roads, had the permanent-way in a very
+bad state. The rails proper, with supplementary angle-plates, rested
+direct upon the cross-girders, which were decidedly light, and the whole
+floor had much "life" in it, the ill-effect of which was shown in
+thirteen breaks in the angle-plates, in each case near their ends,
+generally at holes.
+
+It appears probable that severe stresses may be thrown upon the parts of
+a floor, whether placed at the level of the bottom booms or of the top,
+by changes of length in the booms due to stress. The author has,
+unfortunately, no direct evidence to offer in reference to this, tending
+either for or against the contention. If an unplated floor of cross and
+longitudinal girders of usual arrangement be at the bottom boom of a
+large bridge, as the boom lengthens with the imposition of load upon the
+bridge, all the cross-girders from the centre towards the abutments will
+be curved horizontally, the middle portion being restrained by the
+longitudinals from moving bodily with the ends. Each cross-girder except
+that at the centre, if there be one, will thus present a figure in plan,
+concave towards the abutment to which it is nearest. This will be
+accompanied by stressing of the connections, and a transfer to the
+longitudinals of as much of the tensile stress properly belonging to the
+booms as the stiffness of the cross-girders may communicate.
+
+This in itself will hardly be considerable, and will be the less on
+account of a slight yielding which may be expected at the end
+connections of each longitudinal; but the effect upon the cross-girders
+by horizontal bending will be much marked. If the case be supposed of a
+200-feet span in steel at ordinary loads and stresses, carrying one line
+of way, with cross-girders 20 feet apart, and having no floor-plates, it
+may be ascertained, neglecting for the moment any slight yielding of the
+longitudinal girder connections, that upon the bridge taking its full
+live load there will be the following approximate results: Movement at
+each end of the end cross-girders of 3/10 inch, equivalent to a force of
+7-1/2 tons, tending to bend them horizontally, and a mean stress on the
+outer edges of the girders, 12 inches wide, of 8 tons per square inch
+due to flexure, which, compounded with the ordinary flange stresses,
+will seem to give rather alarming results. There will also be a
+longitudinal stress in the rail-girders, at centre part of bridge, of
+3/4 ton per square inch. Normal elongation of the longitudinal girder
+bottom flanges, and compression of the top, modifies the figures
+unfavourably as to the cross-girder top flange. Yielding of the
+connections named before has been neglected in arriving at these
+stresses. If they are sufficiently accommodating to give freely, to a
+mean extent, as between the top and bottom of each joint, of 1/29 inch,
+these results will disappear. It is evident, however, that we cannot
+rely upon good work yielding without the existence of considerable
+forces to cause it. In the issue it is justifiable to apprehend that the
+flexing and stressing of the cross-girders will be considerable.
+
+The most favourable case has been taken; if now it is assumed that the
+floor has continuous plating, the results would seem to be much more
+astonishing. It will appear on this supposition that the boom stresses,
+instead of being taken wholly by the booms, are about equally divided
+between these and the floor structure, each cross-girder connection
+communicating its share of boom stress to the floor, which for the end
+cross-girders will approach 40 tons at each connection--considerably
+more than the vertical reaction under normal loads.
+
+Palpably, these conclusions must be greatly modified by the yield of
+longitudinal girder ends, and slip of the floor rivets in transverse
+seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the
+stress at each, as estimated, would be sufficient to induce shear of
+about 6 tons per square inch--more than enough to cause "slip." After
+making this allowance, it is still evident there must be very serious
+forces at work about the ends of cross-girders under the conditions
+supposed, probably not less than one half the amounts named, as with
+this reduction the floor rivets should not yield, given reasonably good
+work. It is to be observed that the effect of live load only has been
+introduced, on the presumption that the longitudinals and floor-plating
+have not been riveted up till the main girders have been allowed to
+carry the major part of the dead load; but even this cannot always be
+conceded. The deduction appears to be that the floor and cross-girder
+connections should be studied with special reference to these possible
+effects, either with the object of rendering the communication of these
+forces harmless, or making the floor so that it shall take little or no
+stress from the main booms, by arranging joints across the floor
+specially designed to yield, the ends of longitudinals being schemed
+with the same object. Where there is no plating, the case is, perhaps,
+sufficiently provided for by making the cross-girders narrow, and the
+longitudinal girder connections flexible, or by putting these girders
+upon the top of the cross-girders, when stretching of the bottom flanges
+of the rail-bearers under load may be expected, within a little, to keep
+pace with the lengthening of the main booms.
+
+It would appear that light pressed troughs running across the
+longitudinals would, by yielding in every section, also furnish relief,
+as compared with the rigidity of flat plates.
+
+By placing the floor at a level corresponding to the neutral axis of the
+main girders, the communication of stress to the floor may be avoided;
+but it seldom happens that there is so free a choice as to floor height
+relative to the girders. This solution is, therefore, of limited
+application.
+
+It is obvious that somewhat similar effects must obtain to those
+considered in detail, when the floor structure lies at the level of top
+booms, but with forces of compression from the booms to deal with,
+instead of tension.
+
+
+
+
+CHAPTER IV.
+
+BRACING.
+
+
+Bracing, whether to strengthen a structure against wind, to insure the
+relative positions of its parts, or for any other purpose, cannot be
+arranged with too great care and regard to its possible effects. Forces
+may be induced which the connections will not stand, with loose rivets
+as a consequence, and inefficiency of the bracing itself; or, the
+connections holding good, stresses in the main structure may, perhaps,
+be injuriously altered.
+
+To take a not uncommon case, let us suppose a bridge consisting of four
+main girders placed immediately under rails of ordinary gauge, and
+braced in vertical planes only, right across from one outer girder to
+the other. If the roads were loaded always at the same time, nothing
+objectionable would result; but, as a fact, this will be the exception.
+When one pair of girders only takes live load, and deflects, the bracing
+under the six-foot will endeavour to communicate some part of this load
+to the other pair of girders. If the bracing is so designed that some
+correctly calculated portion of the load can be transferred in this
+manner, without over-stressing the bars and riveted connections, there
+will be no harmful consequences; but if not, the bracings will most
+probably work at the ends; this, indeed, is what frequently happens.
+There is one other effect which will ensue, if the bracing is wholly
+efficient; a certain twisting movement of the bridge will occur, which
+increases the live load upon the outer girder on the loaded side of the
+bridge to the extent of 10 per cent., with a corresponding lifting force
+at the outer girder on the unloaded side. These amounts are not serious,
+but wholly dispose of any advantage it is conceived will be gained by
+causing the otherwise idle girders to act through the medium of the
+bracing. In road bridges of similar arrangement, over which heavy loads
+may pass on any part of the surface, it is clear that the use of bracing
+between girders should not be taken as justifying the assumption that
+the load is distributed over many girders, and correspondingly light
+sections adopted, unless the effect of twisting on the whole bridge is
+also considered, and justifies this view; for, as already stated in the
+case of the railway bridge, the net result may be to increase the girder
+stresses instead of reducing them. Generally, it may be deduced that the
+better plan for railway bridges is to brace the girders in pairs,
+leaving, in the case supposed, no bracing between the two middle
+girders, though there will be no objection to connecting these by simple
+transverse members of no great stiffness, to assist in checking lateral
+vibration. For road bridges of more than five longitudinal girders,
+equally spaced, it may be advantageous to brace right across, the
+twisting effect with this, or a greater, number of girders not, as a
+rule, leading to any increase of load on any girder. Figs. 22 to 25 give
+the distribution of live load, placed as shown, for 3, 4, 5, and 6
+girders.
+
+It is to be observed that these statements do not apply to cases where
+there may be also a complete system of horizontal bracing, the effect of
+which, in conjunction with cross diagonals, may be greatly different,
+with considerable forces set up in the bracing, and a modification of
+girder stresses.
+
+These effects may be so considerable as to call for special attention in
+design where such an arrangement is adopted.
+
+[Illustration: FIG. 22.]
+
+[Illustration: FIG. 24.]
+
+[Illustration: FIG. 23.]
+
+[Illustration: FIG. 25.]
+
+Somewhat similar straining to that first indicated may occur in bracings
+placed between the girders of a bridge much on the skew. If this is, on
+plan, at right angles to the girders, as is commonly and properly the
+case, the ends will evidently be attached to the girders at points on
+their length at different distances from the bearings, which points,
+even with both girders loaded, deflect dissimilar amounts, and the
+bracing will, if at one end attached near a rigid bearing, transfer some
+part of the load from one girder to the other, notwithstanding that
+both girders may be of the same span and equal extraneous loading. It
+would not be difficult to ascertain the amount of load so transferred
+from a consideration of the relative movements if free, and the loads on
+the two girders necessary to render these movements equal, if the
+deflections were simply vertical; but as there will be some twisting and
+yielding of the girders on their seats, the calculation becomes
+involved. If the bracing is placed at about the middle of the girders,
+the effects noted will be greatly reduced; first, because the difference
+of movements near the centre will be less; second, any given difference
+will correspond to a smaller transference of load; and, third, because
+each girder will there be more free to twist than at the ends. It
+therefore appears that bracings between the girders of a skew bridge
+should not be placed near the bearings, though they may be put, with
+much less risk of injury, near the middle.
+
+Cross-girders on a skew bridge are subject to forces somewhat similar to
+those which may affect bracing, rendering it desirable to design their
+attachments in a manner which shall not aggravate the matter, but rather
+reduce the effects of unequal vertical displacement of their ends where
+secured to the main girders.
+
+Crossed flat bars as bracing members are objectionable on account of
+their tendency to rattle, after working loose; but as this effect only
+ensues in bracing which has first become loose (it being assumed that
+the bars in any case are connected where they cross), this objection is
+not itself vital, though greater rigidity is easily obtained by making
+all such members of a stiff section.
+
+Defective bracing between girders, from neglect of the very considerable
+forces it may be called upon to communicate, is very common; the writer
+has seen many such cases, of which one is here illustrated in Fig. 26.
+
+[Illustration: FIG. 26.]
+
+This bridge, of the section shown, and 85 feet span, had very light web
+structure. The bracings, of which there were two sets, were wholly
+inefficient, the end rivets being loose in enlarged holes. Upon the
+passage of a train there was a positive lurching of the girder tops from
+side to side. The integrity of the bridge was really dependent upon
+such stiffness as there was in the girders, and unplated floor.
+
+A common but indifferent method of keeping the top members of main
+girders in line is by the use of overhead girders alone, frequently
+curved to give the requisite clearance over the road. This cannot be
+considered as wholly inefficient, as sometimes maintained, since it is
+evident that the closed frame formed by the floor beams, the web members
+of the main girders, and the overhead girder itself, must take a greater
+force to distort it than would be necessary to cause deformation of a
+corresponding degree, in an open frame formed by the omission of the
+overhead girder; but it is not a method to be recommended, its precise
+utility is difficult to estimate, and, if the cross-girder attachments
+are of a rigid character, tends to increase the stresses induced at
+those connections. The latter consideration is, however, not applicable
+to this arrangement alone. All overhead bracing favours this by
+restraining the tendency of the top booms to cant inwards when the floor
+beams are loaded; and though this restraint may be quite harmless, it is
+desirable that close attention be given to these effects in designing
+bridges which make a complete frame more or less rigid in its character.
+"Sway" bracing, sometimes introduced at right angles to the bridge
+between opposite verticals, tends to emphasise these effects by
+rendering the cross-section of the bridge still stiffer, besides making
+it a matter of difficulty to ascertain how much of the wind forces on
+the top boom is carried to the abutment by the top system of bracing,
+and how much by the floor. The author does not, however, mean to suggest
+that it cannot be used with propriety, but rather that extreme care is
+desirable in considering its ultimate effect on the rest of the
+structure.
+
+For girders of moderate depth there may be on these grounds a distinct
+advantage in abandoning overhead bracing, and securing rigidity of the
+top boom, and adequate resistance to wind forces, by making the
+connection between the cross-girders and the web members sufficiently
+good to insure, as a whole, a stiff [U]-shaped frame; but this, with the
+ordinary type of rocker arrangement under the main girder bearings, will
+not be entirely free from objection, as canting of the girders due to
+floor loading will throw extreme pressure on the inner end of each
+rocker. There appears to be no reason why the cylindrical knuckle should
+not in this case be supplanted by a cup hinge, allowing angular movement
+of the girder bearing in any plane.
+
+[Illustration: FIG. 27.]
+
+The efficient stiffening of light girders, as in the case of
+foot-bridges, from the floor, where this is at the bottom flanges,
+renders very narrow top booms permissible. This is a decided advantage
+where lightness of appearance is aimed at; but it is not unusual to see
+an attempt made in this direction by introducing gusset plates of very
+ample proportions between vertical members of the girders, and the
+projecting ends of flimsy transoms, carried beyond the width of the
+bridge proper, these being of a section wholly out of proportion to the
+brackets they are supposed to secure. Whatever may be the amount of
+strength necessary at the point A, in Fig. 27, there should not be less
+throughout the transom from one girder to the other. The degree of
+strength and stiffness required in this member, and in the vertical
+stiffeners is not, as a rule, great. Information to enable this question
+to be dealt with as a matter of calculation is somewhat scanty; but it
+would appear to be sufficient to insure safety that, for an assumed
+small amount of curvature in the compression member, the forces outwards
+corresponding to this curvature, due to thrust, should be resisted by
+verticals and transoms of strength and stiffness sufficient to restrain
+it from any further flexure. It will, of course, be necessary also to
+take care that the compression member is good as a strut between the
+points of restraint. A simple and sufficiently precise method of dealing
+with this question is much needed. In cases where the floor weight rests
+on the flange projection, it is also necessary to give the transom
+additional strength to an extent enabling it to resist the twisting
+effort between any two of these transverse members; further, resistance
+to wind on the girder has to be provided in both transoms and verticals.
+
+It may be hardly necessary to insist that bracing intended to stiffen a
+structure against wind, local crippling, or vibration, should be made
+complete, not stopping short at some point, because it cannot
+conveniently be carried further, as is sometimes done, unless the
+strength of those parts of the structure through which the forces from
+the bracing must be communicated to the abutments is sufficiently great,
+considered with reference to other stresses in those parts which have
+also to be endured.
+
+Bracing stopped short in this way, making only the central part of a
+bridge rigid, may have the effect of increasing the forces to which the
+unstiffened end members would otherwise be liable. Such a structure
+would evidently be much stiffer against wind-gusts than if no bracing
+existed--the resistance to a blow would be increased; but the power to
+maintain that greater resistance being confined to the intermediate
+bays, the unbraced ends would be subject to greater maximum forces than
+if bracing were wholly omitted. The net effect may still be better than
+with no bracing, the point raised being simply that of an increase of
+stress in particular end members.
+
+In the bracing of tall piers, the rising members of which will be
+subject to any considerable stress, if the diagonal members are not
+finally secured when the piers are under their full load, or an initial
+stress of proper amount induced in those members, the effect of loading
+will be to render them slack; so that an appreciable amount of movement
+at the top may occur before it can be limited by the efficient action of
+the bracings. This effect under blasts of wind or continual passage of
+trains may, indeed, be dangerous. Similar considerations apply to the
+top wind bracing of deep girder bridges, influencing also the bottom
+bracing in a contrary manner, which calls for attention in fixing the
+unit stresses for such members.
+
+The bracing of sea-piers is very liable to slacken if made with
+pin-and-eye ends, as is often done for round rods. The detail presents
+advantages in erection, but is not altogether satisfactory in practice.
+Such connections are continually working. In the finest weather, with
+the sea quite smooth but for an almost imperceptible wave movement, the
+lower parts of such structures will be found, as a rule, to have some
+slight motion. This is very trying to bracing; nor is there room for
+surprise when it is considered that these oscillations, occurring at
+about ten to each minute, never wholly cease, and amount in the course
+of one year to over five million in number.
+
+Bracing attached in such a manner that there can be no initial slack, or
+slack due to wear under endless repetitions of small amounts of stress,
+will have a much better chance to keep tight. The advantage presented
+by round rods in offering little surface to the water, is more than
+negatived by inefficiency of the usual attachments for such rods.
+
+The author has observed that bracing of members possessing some
+stiffness, and with good end attachments to ample surfaces, appears to
+stand best in ordinary sea-pier work. For such structures the bracing
+should consist of a few good members, with a solid form of attachment,
+rather than of a multiplicity of lighter adjustable members, which will
+commonly give great trouble in maintenance; being very possibly also, in
+the case of sea-pier work, in unskilled hands. If round rods must be
+used, they will stand much better if made of large diameter.
+
+Before leaving the subject of bracing, it may not be out of place to
+refer to wind pressure, as this may so much affect the proportioning of
+the members.
+
+Some years since the author had occasion to examine a number of
+structures with respect to their stability. Of foot-bridges from 60 feet
+to 120 feet long, three or four, when calculated on the basis
+recommended by the Board of Trade as to pressures upon open-work
+structures, worked out at an overturning pressure of from 18 lb. to 22
+lb. per square foot. These bridges had been many years in existence; it
+is, therefore, fair to assume that no such wind in the direction
+required for overturning had expended its force upon them as to the
+whole surface.
+
+[Illustration: FIG. 28.]
+
+Particulars were taken in 1895 of a notice-board, presenting about 12
+square feet of surface, which was blown down in the great storm of March
+24 of that year, at Bilston, in Staffordshire. It was situated at the
+foot of a slight slope, over which the wind came, striking the
+obstruction at right angles. The board was mounted on two oak posts of
+fair quality and condition, which broke near the ground at bolt holes
+(see Fig. 28). The force required to do this, at 9000 lb. modulus of
+rupture--a moderate value--corresponds to 50 lb. per square foot on the
+surface exposed above the break.
+
+In the same neighbourhood, at the same time, considerable damage was
+wrought in overturning chimney stacks, to buildings and roofs; the
+general impression in the locality being that the storm was of
+exceptional, even unprecedented, violence. Bilston, it should be noted,
+lies high.
+
+At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27
+lb. was registered. In another part of the country it is said to have
+been 37 lb. Wind is so capricious in its effects over small areas as to
+render it probable that the maximum pressures have never been recorded;
+but this is a matter of little importance where general stability and
+strength only are concerned. The instances cited, though by themselves
+insufficient to throw much light on the question, may be of use in
+connection with other known examples.
+
+
+
+
+CHAPTER V.
+
+RIVETED CONNECTIONS.
+
+
+Considerable latitude is observable in the practice of engineers in the
+use of rivets. Numberless experiments to determine the resistance of
+riveted connections have from time to time been made, but these are not
+to be considered by themselves as final, when the results of experience
+in actual construction, are available for further enlightenment.
+
+The class of workmanship so largely influences the degree in which
+rivets will maintain their integrity that it is only by the observation
+of a large number of cases, including all degrees of workmanship, that
+any reliable conclusions may be drawn. In this respect laboratory
+experiments have an apparent advantage, as the conditions may be kept
+sensibly the same; but, on the other hand, no such investigation
+reproduces the circumstances of actual use, which alone must in the end
+determine the utility of any inquiry for practical application.
+
+The author has studied the particulars of a number of cases to ascertain
+under what conditions as to stress, having due regard to the effects of
+vibration, rivets will remain tight, or become loose. Every loose rivet
+that may be found cannot, of course, be taken as being due to excessive
+stress; the more frequent cause is indifferent work, evidenced by the
+fact that neighbouring rivets will frequently be found quite sound,
+though the failure of some will cause a greater stress upon the
+remainder. When rivets loosen as the direct result of over-stress, it is
+usually by compression of the shank and enlargement of the hole, or by
+stretching of the rivet and reduction of its diameter. Instances of
+failure by partial or complete shear are extremely rare; indeed, the
+author has never yet found one, though when a rivet has first worked
+loose, as a result of excessive bearing pressure or bad work, it is not
+uncommon to find it cut or bent as an after consequence.
+
+In estimating stresses at which rivets have remained tight, or loosened,
+as the case may be, examples have generally been chosen in which there
+could be no reasonable doubt as to the amount of those stresses by the
+ordinary methods of computation. This is clearly most important, as, if
+any appreciable uncertainty remained as to the degree of stress, the
+results deduced would be of little value. For this reason those
+instances in which the loads upon girders, or parts of girders, may find
+their way to the supports by more than one route, are to be regarded
+with caution, as are those in which full loading possibly never obtains,
+but which may, on the other hand, perhaps have been frequent. The
+working diameter of the rivet as it fills the hole has been used in
+making the computations; in some cases from direct measurement from
+particular rivets, in others with a suitable allowance for excess
+diameter of hole, according to the class of work under consideration.
+
+Dealing first with main girders, it may be said that rivets attaching
+the webs of plate girders to the flange angles rarely loosen, though
+subject to considerable stress. In illustration of this may be named a
+bridge for two lines of way, 85 feet effective span, having two main
+girders with plate webs, and cross-girders resting on the top flanges,
+previously referred to (see Fig. 26).
+
+The girders, which were 6 feet 9 inches deep, had a bearing upon the
+abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches
+pitch. There is in a case of this kind some little uncertainty as to
+what is the stress on the flange angle rivets at, or very near to, the
+bearings; but, taking the vertical rows of rivets at the web joints near
+the ends as presenting less uncertainty, the stress per rivet works out
+at 4.8 tons, being 4 tons per square inch on each shear surface, and 11
+tons per square inch bearing pressure upon the shank in the web plate,
+which was barely 1/2 inch thick. This bridge was frequently loaded upon
+both roads, but with one road only carrying live load, the stresses in
+the more heavily loaded girder would be fully 90 per cent. of those
+obtaining as a maximum. There was on this bridge, which had been in use
+31 years, considerable movement and vibration.
+
+It is by no means uncommon to find cases of rivets in main girders
+taking 11 tons per square inch bearing pressure--occasionally more--and
+remaining tight. As furnishing an instructive, though slightly
+ambiguous, instance of rivets in single shear, may be cited a bridge not
+greatly less than that just referred to, of about 65 feet span, carrying
+two lines of way, there being two outer and one centre main girder of
+multiple lattice type, with cross-girders in one length 4 feet apart,
+riveted to the bottom booms of the main girders; these rivets, by the
+way, were in tension. The floor was plated, the road consisting of stout
+timber longitudinals, chairs, and rails (Fig. 29).
+
+[Illustration: FIG. 29.]
+
+It should be noted that there is in this case some difficulty in
+ascertaining the precise behaviour of the cross-girders, affecting the
+proportion of load carried by the outer and the inner main girders.
+Strict continuity of all the cross-girders could only obtain if the
+deflection of the main girders were such as to keep the three points of
+suspension of each cross-girder in the same straight line. A close
+inquiry showed that this was very far from being the case, and that
+while each cross-girder at the centre of the bridge would, under load,
+by relative depression of the middle point of support, be reduced to
+the condition of two simple beams, those at the extreme ends of the span
+would behave as continuous girders.
+
+With both roads carrying engine loads equal to those coming upon the
+bridge, the author estimates that for the centre main girder the shear
+on the rivets of the end diagonals, secured by one rivet only, was 14.9
+tons per square inch, and the bearing pressure 16.3 tons; the flange
+stress being 7.1 tons per square inch net. The outer main girders are
+most heavily stressed when but one road, next to the outer girder
+considered, carries live load. For this condition the stresses work out
+at 9 tons per square inch shear on the rivets of the end diagonals, and
+9 tons bearing pressure, the flange stress being 5.7 tons per square
+inch on the net section.
+
+Without intending to throw any doubt upon the substantial truth of these
+results, it must be admitted that instances of greater simplicity of
+stress determination are much to be preferred. For purposes of
+comparison, but not as having any other value, the results have also
+been worked out on the supposition of all cross-girders acting each as
+two simple beams, and also for strict continuity, and are here
+tabulated, together with the conclusions given above.
+
+The cross-girders were moderately stressed, and the tension on the
+rivets attaching them to the main girders probably did not exceed 3 tons
+per square inch.
+
+It should be pointed out that the traffic over the bridge was small. The
+centre main girder but seldom bore its full load, though at all times
+liable to receive it. Much importance cannot, therefore, be attached to
+the results for this girder, other than as showing how a structure may
+stand for many years, though liable at any time to the development of
+stresses which would commonly be regarded as destructive, or nearly so.
+
+EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS.
+
+  ---------------------------------+-----------+------------+---------
+                                   |   Cross-  |   Cross-   |
+                                   |  Girders  | Girders as | Correct
+                                   | as Simple | Continuous | Results.
+                  --               |   Beams.  |   Beams.   |
+                                   +-----------+------------+---------
+                                   | Stress in Tons per Square Inch.
+  ---------------------------------+-----------+------------+---------
+  Centre girder, 63 ft. span (both |           |            |
+  roads loaded):                   |           |            |
+    Rivets in diagonals--Shear     |    13.7   |    17.2    |  14.9
+          Do.            Bearing   |           |            |
+                         pressure  |    15.0   |    18.8    |  16.3
+                         Flange    |           |            |
+                         stress    |     6.8   |     8.5    |   7.1
+                                   |           |            |
+  Outer girder, 66 ft. span (near  |           |            |
+  road loaded):                    |           |            |
+    Rivets in diagonals--Shear     |     9.6   |     8.2    |   9.0
+          Do.            Bearing   |           |            |
+                         pressure  |     9.6   |     8.2    |   9.0
+                         Flange    |           |            |
+                         stress    |     5.9   |     5.1    |   5.7
+  ---------------------------------+-----------+------------+---------
+
+The material and workmanship of the bridge were good. The rivets of the
+centre girder end diagonals, 1 inch in diameter, were originally 7/8
+inch, but on becoming loose were cut out, the holes reamered, and
+replaced by the larger size, which remained tight, and to which the
+stress figures apply. The rivets in the diagonals near the centre, 7/8
+inch in diameter, which were subject to reversal of stress, occasionally
+worked loose, and were more than once replaced. The riveting in the
+outer girder diagonals, subject to smaller stresses, much more
+frequently developed, also gave trouble, particularly those liable to
+counter stresses.
+
+Apart from looseness of rivets, the general appearance and behaviour of
+the bridge, which had been in existence about twenty years, was not
+suggestive of any weakness.
+
+Of smaller girders, an example showing the necessity for care in
+discriminating, if it be possible, between looseness of rivets resulting
+from over-stress and that due to other influences may first be quoted.
+Two trough girders, of 11 feet effective span, each of the section shown
+in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle,
+with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch
+pitch, showed certain defects, of which one, it may be incidentally
+mentioned, was a cracked web (Fig. 31). From the nature of the
+arrangement the lower web rivets, which were loose, would receive the
+first shock of the load coming upon the span, but there were evidences
+indicative of original bad work. The angle bars gaped, suggesting that
+these had first been riveted to the bottom plate, and left sufficiently
+wide to allow the web to be afterwards inserted, the rivets failing to
+pull the work close, and then readily working loose. Here there is
+considerable uncertainty as to how much of the loosening is to be
+attributed to bad work, and how much to stress. It may, however, be
+remarked that whatever bearing stress was the ultimate result of the
+load hammering on the lower angle flanges, loosening rivets never
+perhaps really tight, the stress of 7 tons per square inch bearing
+pressure on the upper rivets, though aggravated by considerable
+impactive force, was not sufficient to loosen these. The girders were
+taken out after being in place sixteen years.
+
+[Illustration: FIG. 32.]
+
+[Illustration: FIG. 30.]
+
+[Illustration: FIG. 31.]
+
+An instance of undoubted excessive bearing pressure was found in the
+cross-girders of a bridge, mentioned on p. 15, of which so many web
+plates were cracked. This bridge, carrying two lines of way, had outer
+main girders, and long cross-girders with 1/4-inch webs and 3/4-inch
+rivets, 4 inches pitch. The rivet stresses work out at 4.3 tons per
+square inch on each shear surface, and 24 tons per square inch bearing
+pressure. For one road only being loaded, the latter figure falls to
+18.5 tons. The traffic over this bridge, twenty years old, was
+considerable, rapid, and heavy. It is hardly necessary to add that a
+large number of the rivets were loose, one of which is shown in Fig. 32.
+
+[Illustration: FIG. 33.]
+
+To take another case relating to a floor system of extremely bad design
+(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor
+having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches
+deep, supporting hog-backed trough longitudinals. The cross-girders were
+at their ends but 6-3/4 inches deep, the distance from the bearing of
+cross-girders to centre of longitudinals carrying a rail being 2 feet 10
+inches, in which length were eight rivets in the web and angles at the
+top, and six at the bottom, all 3/4 inch in diameter.
+
+The shear stress on the upper rivets works out at 7.3 tons per square
+inch on each shear surface, the bearing pressure 20.6 tons per square
+inch. On the lower rivets the shear stress becomes 9.7 tons, and the
+bearing pressure 27.4 tons, per square inch. Care was exercised in
+computing these stresses, that part of the bending moment carried by the
+web being allowed for, but it must be admitted that the result is,
+probably, approximate only. The sketch here given shows the cross-girder
+end and section. The rivets, though in double shear, were, as might be
+expected, loose, notwithstanding that the traffic over the bridge was
+moderate, and quite slow. The floor system was remodelled after twelve
+years' use.
+
+In illustration of the behaviour of rivets in the ends of long
+cross-girders, both shallow and weak, and many years in use under heavy
+traffic, may be cited connections having end angle bars to the
+cross-girders, with six rivets through the web of main girders. The
+bearing pressure worked out at 7.8 tons per square inch. Many rivets
+were loose, but it should be remarked that the workmanship was not of
+the best class, and the cross girders flexible: a characteristic very
+trying to end rivets, and inducing a stretch in some, already referred
+to as a possible cause of loosening. This will be apparent if the
+probable end slope of weak girders be considered. The author concludes
+that this inclination should not, for ordinary cases, exceed 1 in 250;
+but the ratio must largely depend upon the degree of rigidity of the
+part to which the connection is made. It is commonly regarded as bad
+practice to submit rivets to tension, yet this is frequently, though
+unintentionally, permitted in end attachments, without any attempt to
+limit the amount of tension. With suitable restrictions, there appears
+no serious objection to rivet tension for many situations.
+
+Another instance of cross-girder end connections of a different type is
+illustrated in Fig. 34.
+
+The main girders of the bridge were 12 feet apart, each cross-girder end
+carrying its share of the half of one road. The mean bearing pressure
+upon the rivet shanks works out at 5.8 tons per square inch for the six
+rivets of the original joint, but in the particular joint shown some of
+the rivets had loosened, making the bearing pressure upon the remainder
+about 8.7 tons per square inch. It is apparent there must have been
+considerable stress on the top and bottom rivets which loosened. These
+two rivets would also, because of difficult access, be in all likelihood
+insufficiently hammered up. The joints worked rather badly; the loose
+rivets had "cut" to a considerable extent, a process materially assisted
+by the gritty nature of the ballast (limestone), particles of which,
+getting into the joint, contributed to the sawing action; this had
+clearly been taking effect for some considerable time. (See Fig. 35.)
+
+[Illustration: FIG. 34.]
+
+[Illustration: FIG. 35.]
+
+The two cases of cross-girder ends given are both rather exceptional in
+character, and in each case the defects appear to be due to general bad
+design and workmanship rather than to any serious excess of bearing
+pressure. This may be illustrated by taking the common case of
+cross-girders, 2 feet deep, carrying two roads, and having end angle
+irons riveted to the web and stiffeners of the main girders by ten
+rivets in single shear at each end. In this example, which is, for old
+work, simply typical, and does not relate to any specific instance, the
+bearing pressure on the rivets will work out at from 6 to 8 tons per
+square inch, and will seldom be accompanied by looseness of rivets, and
+then only as a result of faulty work.
+
+Some sketches of rivets taken from old bridges have already been given
+in connection with the cases to which they belong; a few others are here
+shown (Figs. 36 to 40) to further illustrate what may be the actual
+condition of rivets after some years' use, and how different from the
+ideal rivet upon which calculations are based. These are, however, bad
+instances.
+
+[Illustration: FIG. 36.]
+
+[Illustration: FIG. 37.]
+
+[Illustration: FIG. 38.]
+
+[Illustration: FIG. 39.]
+
+[Illustration: FIG. 40.]
+
+It should be noticed that rivets may, if in double shear, be loose in
+the middle thickness, due to enlargement of the hole in the central part
+and compression of the rivet, and yet show no sign of this by testing
+with the hammer. There is, however, generally marked evidence of another
+kind in the "working" of the inner part, as, for instance, the web of a
+plate girder, in which case a discoloration due to rust is to be found
+along the edges of the angle bars, or a movement may be detected on the
+passage of live load. Red rust is, in fact, frequently an indication of
+something wrong, when no other evidence is apparent. In plate girders
+having [T] or [L] bars brought down and cranked on to the top of shallow
+cross-girders, it is not uncommon to find the rivets attaching these
+bars to the cross-girder tops loose, due to causes already dealt with.
+The riveted connection should, as to strength, bear some relation to the
+strength and stiffness of the parts secured, if the rivets are to remain
+sound.
+
+It may be well to give here a summarised statement of the results
+already named, for purposes of ready reference. These by themselves are
+not sufficient to enable working stresses to be deduced, though they are
+instructive. The author has found many instances of shear and bearing
+stresses in excess of those usually sanctioned, under which the rivets
+behaved well, but is not now able to give precise particulars of these.
+
+EXAMPLES OF RIVET STRESSES.
+
+  ---------+-----+---------+------+------+--------+-----------------
+     --    |Span |  Where  |Shear |Single|Bearing | Tight or Loose.
+           | in  |  Found. |Stress|  or  |Pressure|
+           |Feet.|         |  in  |Double|in Tons |
+           |     |         | Tons |Shear.|  per   |
+           |     |         |  per |      | Square |
+           |     |         |Square|      | Inch.  |
+           |     |         |Inch. |      |        |
+  ---------+-----+---------+------+------+--------+-----------------
+  Main    {|  85 |   Web   |  4.0 |   D  |  11.0  | Tight.
+  girders {|  66 |Diagonals|  9.0 |   S  |   9.0  | Many loose.
+          {|  63 |    "    | 14.9 |   S  |  16.3  | Tight generally.
+           |     |         |      |      |        |
+          {|  11 |   Web   |  1.4 |   D  |   7.0  | Tight.
+  Small   {|  26 |    "    |  4.3 |   D  |  24.0  | Many loose.
+  girders {|  11 |    "    |  7.3 |   D  |  20.6  | Loose.
+          {|  11 |    "    |  9.7 |   D  |  27.4  | Loose.
+           |     |         |      |      |        |
+  End     {|  27 |   Ends  |  5.4 |   S  |   7.8  | Loose.
+  connec- {|  12 |    "    |  1.8 |   D  |  {5.8  |}Many loose.
+  tions   {|     |         |      |      |  {8.7  |}
+           |     |         |      |      |        |
+  (Type    |     |         |      |      |        |
+  case)    |  26 |    "    |  4.8 |   S  |   7.0  | Tight.
+  ---------+-----+---------+------+------+--------+-----------------
+
+It is probable that the fact of a rivet being in single or in double
+shear largely affects its ability to resist the effects of bearing
+pressure, as commonly estimated. In the first case, the rivet-shank must
+bear heavily on the half-thickness of the plates or bars through which
+it passes, rather than on the whole thickness; and it is to be supposed
+that under this condition it will work loose at a lower average stress
+than if it were in double shear, and the pressure better distributed.
+
+[Illustration: FIG. 41.]
+
+[Illustration: FIG. 42.]
+
+The author has no very definite information in support of this
+contention, but suggests that for double shear the permissible bearing
+pressure may probably be as much as 50 per cent. greater than for rivets
+in single shear; the difference being made rather in the direction of
+increasing the allowable load on double-shear rivets, than in reducing
+that upon rivets in single shear. The propriety of this is evident when
+it is considered that the practice has commonly been to make no
+distinction, so that whatever bearing pressures are found to be
+sufficient for both cases may be increased for those capable of taking
+the greater amount. Figs. 41 and 42, here given, illustrate the
+behaviour of rivets under the two conditions.
+
+With reference to the amounts of the stresses to which rivets may be
+subject, the author concludes, as a result of his experience, coupled
+with a consideration of known laboratory tests, that for all dead load
+these may be quite prudently higher than is frequently taken. For iron
+the shear stress to be 10 per cent. less than the stress of parts
+joined; and the bearing pressure--for single-shear rivets, 20 per cent.;
+and for double-shear rivets, 80 per cent. greater. For ordinary mild
+steel the shear stress to be 20 per cent. less than the stress in parts
+connected, and the bearing pressure equal to it for single-shear rivets;
+and 50 per cent. more for rivets in double shear, though the two latter
+values may probably approach those for wrought iron in steel of the
+higher grades sometimes used in bridge-work. For live load, or part live
+and part dead load, the same rules may apply, the reduction of the
+nominal working stress, arrived at by any one of the methods in use
+which may be adopted, affecting both the parts connected, and the rivets
+connecting them. For reverse stresses it is advisable to keep the shear
+stress in any rivet so low, say 3 tons per square inch, that the
+frictional resistance of the parts gripped by the rivets shall be
+sufficient to prevent any tendency to slip under the influence of the
+smaller of the two forces to which the part is liable, to insure that,
+if brought to a bearing in one direction by the greater force, it shall
+not go back with reversal of stress. This requirement may be open to
+some question with respect to good machine-riveted work, but for
+hand-riveted connections it may certainly be adopted with wisdom.
+
+The following table will show at a glance how the stresses proposed vary
+with the unit stresses governing the main sections.
+
+PROPOSED TABLE OF RIVET STRESSES.
+
+  -----------+-------------+----------------+----------------
+  Unit Stress|             |Bearing Pressure|Bearing Pressure
+      in     |Shear Stress.|for Single-Shear|for Double-Shear
+    Member.  |             |     Rivets.    |    Rivets.
+  -----------+-------------+----------------+----------------
+              _Wrought Iron.--Tons per Square Inch._
+       3.0   |     2.7     |       3.6      |       5.4
+       4.0   |     3.6     |       4.8      |       7.2
+       5.0   |     4.5     |       6.0      |       9.0
+       6.0   |     5.4     |       7.2      |      10.8
+       7.0   |     6.3     |       8.4      |      12.6
+                 _Steel.--Tons per Square Inch._
+       4.0   |     3.2     |       4.0      |       6.0
+       5.0   |     4.0     |       5.0      |       7.5
+       6.0   |     4.8     |       6.0      |       9.0
+       7.0   |     5.6     |       7.0      |      10.5
+       8.0   |     6.4     |       8.0      |      12.0
+       9.0   |     7.2     |       9.0      |      13.5
+  -----------+-------------+----------------+----------------
+
+  NOTE.--Tension on rivets to be limited to one-half the permissible
+  shear stress, the holes being slightly countersunk under snap-head.
+
+It may be objected that the shear stresses in the proposed table are
+somewhat high for wrought iron and steel. This feature is intentional,
+and is supported by the consideration that whereas there may be loss of
+strength in the members of a structure by waste, there is no such loss
+in rivets, if the work is so designed that there shall be no loosening.
+Any allowance that may be desirable for loose or defective field rivets
+is left to be dealt with as may be considered advisable for each
+particular case, the table as it stands being applicable only to
+riveting not below the standard of first-rate hand work.
+
+Cases of loose rivets in main girders over 50 feet span, due to any
+cause but bad work, are extremely rare, unless resulting from the action
+of some other part of the structure. It may be stated broadly that for
+railway bridges of less than perfect design, the nearer the rail, the
+more loose rivets, generally at connections. This is, no doubt, largely
+due to the severe impact of the load, the effects of which are greater
+near the rail, both because of the small proportion of dead load, and
+because this effect has been but little modified by the elasticity of
+any considerable length of intervening girder-work. In addition to this,
+it is quite usual to find the rivets more heavily stressed, even though
+the load be considered as "static," in the floor system than in the
+main-girders, though the reverse should be the case. It is unfortunate
+that those parts which require the best riveting--viz., the
+connections--are commonly dealt with by hand; and for this reason it is
+the more necessary to design these with the greatest care.
+
+Any arrangement which favours the gradual acceptance of stress by one
+part from another will contribute to the integrity of riveted
+connections, and lessen the liability of the material to develop faults.
+In other branches of design this is well recognised, but appears in much
+old bridge work to have been entirely overlooked.
+
+Bridges carrying public roads very seldom furnish examples of loose
+rivets; the conditions are generally much more favourable, impact being
+practically absent, full loading infrequent, and the proportion of dead
+load to live, high.
+
+It is, perhaps, hardly necessary to insist upon rivets being, apart from
+mere considerations of strength, sufficiently near together to insure
+close work and exclude moisture. Outside edge seams should never be more
+widely spaced than 16 times the thickness of the plates; 12 thicknesses
+apart is better. In the case of angle, tee, and channel sections, the
+greater stiffness of the section makes wider spacing allowable up to,
+say, 20 times the thickness; but this must be governed largely by the
+amount of riveting required to pull the parts close together. Where more
+than four thicknesses are to be gripped by the rivets, 3/4 inch in
+diameter is hardly sufficient to insure tight work, and quite unsuitable
+if the plates exceed 5/8 inch thick.
+
+
+
+
+CHAPTER VI.
+
+HIGH STRESS.
+
+
+High stress, provided it be well below that at which immediate injury
+results, or possible failure, is not uniformly objectionable. It may be
+first considered relative to the absolute and elastic limits of
+strength, next with respect to the range of stress, and, finally, with
+regard to the frequency of application. For practical purposes--that is,
+for the continued efficiency of a structure--the limit of elasticity
+must be considered to be the limit of strength, or, more strictly, the
+limit for all those parts of the structure which must, so long as it
+lasts, be liable to the original measure of stress. There may be places
+in a bridge, however, over-stressed only in the earlier period of its
+existence, which, by being over-stressed and suffering deformation,
+permit the origin of this distortion to be harmlessly met in some other
+way. In such a case the injury done to that part does not, of necessity,
+lead to any culminating disaster; indeed, were it not for this
+plasticity it is probable a large number of bridges would fail after
+being in use but a short time. As for riveting, so in dealing with the
+amount of stress to which a member is supposed to be liable, it should
+be clearly understood by what method this has been arrived at, whether
+the value assigned is the actual measure of the stress, or simply the
+conventional amount arrived at in the conventional way; perhaps
+neglecting web section in plate girders, or without regard to the
+various influences which may reduce or increase the nominal amount of
+stress, or including only a partial recognition of those influences. In
+any case quoted the stress named is that at which the author arrives by
+the ordinary methods of computation carefully applied, where these
+appear to be sufficiently precise, unless any qualifying remark be
+added. Extreme flange stress is in special cases computed, first on the
+gross section by estimating the moment of inertia on that basis, and
+deducing the stress at the holes from the ratio of net to gross section
+at the extreme fibres; a method more correct than by reference to the
+moment of inertia of the net section. Any exhaustive refinement in the
+study of stresses is not attempted, both because it is beyond the
+author's powers of analysis, and for the reason that such results are
+not comparable with the results of ordinary methods of calculation in
+practice. Effective spans are taken at moderate values, and all
+exaggeration is avoided.
+
+The effects of impact in any part vary so much with nearness to, or
+remoteness from, the living load, and the frequency of development of
+the maximum stress from all causes acting together is so much affected
+by the same consideration, that it is apparent a nominal stress which
+may be harmless in one part of a bridge may be destructive in some
+other, a statement borne out by observation. Stress, as ordinarily
+stated--i.e., at so much per square inch, uniform across a section--is
+seldom a cause of trouble. In nearly all cases of failure there is an
+accompanying localised destructive stress, either in rivets or
+elsewhere, with crippling or deformation of some essential part. In the
+tension flanges of main girders with uncomplicated stress, this may run
+up to an amount very considerably beyond the ordinary limits without
+producing signs of distress. The same remark applies to the compression
+flanges, if these be in themselves sufficiently stiff, or properly
+restrained from side flexure. In support of the above statement may be
+quoted the following instances relating to wrought-iron structures:--
+
+A bridge of 60 feet effective span, having girders immediately under the
+rails, had a flange stress of 6.3 tons per square inch. Another of 64
+feet span, carrying two lines of way, with outside main girders and
+cross-girders, had the flanges of the former stressed to 6.8 tons per
+square inch. A third, of 76 feet span, of similar construction to the
+last, was stressed in the main girder flanges to 7.5 tons per square
+inch. The webs were not included in the computation; the figures,
+therefore, compare with ordinary practice. In these three cases the main
+girders showed no signs of distress, referable to the results stated,
+though the top flanges in the last case were curved inwards. The effect
+of this flexing of the flange would be, of course, to increase the
+amount of compressive stress along one edge, though to what degree
+cannot now be stated.
+
+[Illustration: FIG. 43.]
+
+[Illustration: FIG. 45.]
+
+[Illustration: FIG. 44.]
+
+A further instance of considerable flange stress occurred in a bridge of
+seven nearly equal continuous spans, 25 feet generally, the end and
+greatest span being 29 feet 6 inches, centre to centre of bearings. Some
+details of the bridge are given in Figs. 43 to 45. The four inner main
+girders under rails were 2 feet deep, with webs 1/2 inch thick over
+piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3
+inches by 3 inches by 5/8 inch. There were also two outer girders of the
+same depth, with single [L] bars. Plate diaphragms of full girder depth
+and particularly stiff were carried right across the bridge at the
+centre of the spans, and over the piers. The girders, though evidently
+designed to be continuous, had very poor flange joints at each bearing,
+of little more than one half the flange strength (see Fig. 45). It is
+doubtful if the girders acted with strict continuity for long after
+erection, as the excessive stress in the rivets of the flange joint
+would, for that condition, have been nearly sufficient to shear them. It
+is probable that this being so, the joints first yielded, relieving the
+bending moment over the piers, and increasing it near mid-span. Whether
+the end spans be considered as strictly continuous with the rest, or as
+simple beams, the maximum bending moments would not greatly differ,
+though occurring for continuity over the pier, for free beams at the
+centre. There is, however, an intermediate condition which makes the
+moments at these two places less than either maximum, but equal to each
+other; a condition of semi-continuity agreeable to a partial efficiency
+of the joints referred to. It is this state which has been calculated,
+giving the minimum stress value that can be accepted. The diaphragm has
+been assumed to transfer to the outer girders a due proportion of the
+load. With this explanation it may now be stated that, under engine
+loads corresponding to those running, the flange stress worked out at
+7.4 tons per square inch tension, web included, or 9.7 tons per square
+inch without considering the web; which stresses, it is more than
+probable, may have been greater. The figures include the consideration
+of anything which may contribute to lowering the stress, and are hardly
+to be compared with those worked to in ordinary design of new work, in
+which it would be quite usual to neglect the assistance of the outer
+girders and the webs, to work to heaviest engine-loads, and possibly
+include an allowance for the effects of settlement. Dealt with in this
+way the girders would seem to be of about one-fourth the strength that
+would be required in the design of a new bridge, in which certain
+elements of strength would be deliberately ignored.
+
+The ironwork was in good condition, there was no ordinary evidence of
+weakness apart from the calculated results, the vibration was distinctly
+moderate, and the deflection, though not recorded, was certainly small.
+The bridge did, indeed, seem somewhat inert under load, and favours a
+suspicion, the author entertains, that old girderwork long overstressed
+may have a sensibly higher modulus of elasticity than newer work at more
+moderate stresses. The traffic was not very considerable, and both
+roads, of the same spans, but seldom loaded at the same time; though
+with this construction of bridge there would in either case be very
+little difference. The author recalls no reason for supposing that the
+piers had yielded in any sensible degree. The bridge was rebuilt after
+some thirty-six years' use.
+
+Stress of considerable amount in the flanges of a latticed main girder
+of 63 feet span has already been noticed in the chapter on "Riveted
+Connections," which for the tension boom worked out to 7.1 tons per
+square inch, the flanges in this case showing no signs of weakness. An
+instance has also been given in dealing with a case of side flexure in
+which the extreme fibre stress was calculated to be 10 tons per square
+inch, the girder recovering its form when relieved of load.
+
+As to stress in cross-girder flanges, an example may be quoted of a
+bridge of 109 feet span, carrying two roads, having outside main
+girders, with cross-girders between; these latter were stressed in the
+flanges to 6.7 tons per square inch (webs not included), if the partial
+distribution among the girders (which were spaced 6 feet apart) by the
+rails and longitudinal timbers be neglected. There is some reason to
+think in this instance that distribution had the effect of reducing the
+stress quoted, as the observed deflection of the cross-girders was
+materially less than that calculated for girders acting independently of
+each other, though this may be in part due to a cause already hinted at.
+Rigidity of the cross-girder ends, where attached to the heavy main
+girders, would also tend to moderate the stress. No very definite
+conclusion can therefore be deduced from this instance.
+
+To take another case of less uncertainty, the bridge of 35 feet span
+(see Fig. 33), referred to in "Riveted Connections," may again be cited.
+The extreme fibre stress in the cross-girder flanges worked out at 6.3
+tons per square inch, web included, or 6.5 tons, exclusive of the web.
+It cannot be said in this example that the girders showed no signs of
+weakness, as the deflection under live load was 1/2 inch on the span of
+11 feet, in addition to a permanent set of 3/4 inch, largely due,
+however, to "working" rivets.
+
+A better and altogether conclusive case of the way in which
+cross-girders may occasionally suffer considerable stress, and show no
+sign, is furnished by two cross-girders, of which some particulars are
+here given. These girders occurred in the floor of a very acute angled
+skew bridge, riveted at one end to the main girders in a manner which
+was very far from fixing the ends, resting at the other end on a masonry
+abutment. The first girder was about 19 feet effective span, 12 inches
+deep in the web, with angle bar and plate flanges. The girders were
+spaced 6 feet apart, and were connected under the rails by [T]-bars,
+cranked down to face the webs, and riveted through. Though these [T]'s
+had little stiffness, yet the frequent vertical movements of the girders
+relative to each other, under passing loads, had broken the majority of
+the [T]-bars at the bends, so that no notice need be taken of these as
+transferring load from any one cross-girder to its neighbour. The floor
+covering consisted of timbers about 4 inches thick, also incompetent to
+transfer any sensible proportion of the load on a girder to others 6
+feet distant. Upon the floor was cinder ballast, with sleepers, chairs,
+and ordinary bull-headed rails. The stress to which the girder was
+liable works out at 8.4 tons per square inch, on the extreme fibres of
+the net section, web included; or 9.1 tons, neglecting the web, under
+engine-loads of a common amount. The other girder had an effective span
+of about 22 feet, as before 12 inches deep in the web, with angle bar
+and plate flanges. The stress per square inch was 10.5 tons, web
+included, or 11.1 tons per square inch, neglecting the web. This girder
+carried three rails, one of which was near to the abutment bearing, so
+that there was no great difference in the stress induced whether all
+three rails were loaded or the pair only. The traffic over the bridge
+was very great, but of moderate speed. It must have been a common
+occurrence for the girders to take the full loads. The heavier engines
+passed scores of times in a day--lighter engines probably one hundred
+times. The bridge was about twenty years old, yet these cross-girders,
+when removed, showed no other sign of age and wear than that due to
+rust.
+
+[Illustration: FIG. 46.]
+
+All the foregoing instances relate to wrought-iron bridges. Two cases of
+steel construction are here added, the first of these furnishing an
+example of high girder stress somewhat remarkable. This was found in a
+trough girder of a strange pattern, of which a section is here given
+(Fig. 46). The bridge to which it belonged carried a siding, over which
+engines of less than the heaviest class sometimes passed at a crawling
+pace. The larger of the two girders carrying the rails was 15 feet 8
+inches effective span. The sides of the trough consisted each of two
+vertical plates, originally 1/2 inch thick, but wasted to an aggregate
+thickness of 5/8 inch. These plates 6 inches deep, were connected at
+their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which
+again were riveted to a bottom plate 16 inches wide, originally 1/2 inch
+thick, wasted to 3/8 inch. Lying in the bottom of the trough, and
+riveted through the inner angle flanges, was a bridge-rail. Assuming
+that the metal retained its elastic properties from top to bottom of the
+section, at whatever stress, this works out at 32 tons per square inch
+at the extreme top fibre, and 15 tons at the bottom, on the net section.
+As puddled steel, of which the girders were made, may have a tenacity of
+45 to 55 tons per square inch, the assumption is probably correct. The
+author has no record of the deflection, but it may be remarked it was
+such that to stand under the girder, with a tank engine passing over,
+required some determination.
+
+A point of additional interest in this little bridge is that, though
+made of steel, it dates as far back as 1861, having been in use
+thirty-two years when removed. The particular variety of steel used was
+known as Firth's puddled. The evidence of this consists in
+correspondence showing that permission had been asked of the controlling
+authority, by the only users of the siding, to apply this material, with
+no evidence of any refusal. At about the same time this steel was also
+used upon the railway concerned in the top flanges of some girders of
+considerable span. The appearance of the trough girders to which the
+foregoing particulars apply was distinctly different to that which might
+be expected in ordinary wrought iron. The top edges of the vertical
+plates were wasted away, smooth, and rounded in a manner strongly
+suggestive of a steely character. Finally, the way in which the girders
+held up to their work for so long is, by itself, conclusive on the
+point. The bridge-rail appeared to be of wrought iron, the different
+modulus of elasticity of which has been included in the calculation upon
+which the preceding results are based. That these girders stood so well
+is, perhaps, largely due to the fact that the load carried by them was,
+though varying within wide limits, practically free from impact, which,
+had the load passed over quickly, would, with girders so small, shallow
+and flexible, have been very sensible.
+
+The second instance of steel construction in which somewhat high stress
+is manifest is that of some steel troughing of the Lindsay pattern, used
+in a bridge built in 1885. The troughs ran parallel to the rails, having
+an effective span of 18 feet 8 inches. The depth of the section (which
+is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span
+of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails.
+
+[Illustration: FIG. 47.]
+
+Assuming this to be carried on six troughs, which corresponds to 11 feet
+3 inches of width, the extreme fibre stress works out at 7.5 tons per
+square inch, under usual engine-loads. The bridge when examined after
+fourteen years' use was in good condition, and at that time but little
+rusted; but the end seam rivets were, as is not uncommon with such
+troughing, loose. The traffic over the bridge was considerable, but not
+at great speed.
+
+On the opposite page are set out the results which have been given, in
+tabulated form, as was done for rivet stresses, to enable ready
+comparison to be made.
+
+EXAMPLES OF HIGH STRESS.
+
+  --------------+-----+---------+---------------+--------+-----------
+                |Span |  Part   |  Stress per   |Tension |Condition.
+                | in  |Stressed.|  Square Inch. |   or   |
+                |Feet.|         +-------+-------+Compres-|
+       --       |     |         | Webs  | Webs  | sion.  |
+                |     |         |  In-  |  not  |        |
+                |     |         |cluded.|  In-  |        |
+                |     |         |       |cluded.|        |
+  --------------+-----+---------+-------+-------+--------+-----------
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |60.0 |Flange   |   ..  |  6.3  |Tension | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |64.0 |   "     |   ..  |  6.8  |   "    | Good.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |76.0 |   "     |   ..  |  7.5  |   "    | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |    {|   "     |  7.4  |  9.7  |   "    |}
+  main girders, |29.5{|   "     |  6.3  |  8.3} |Compres-|}Good.
+  plate         |    {|         |       |     } |sion    |}
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |63.0 |   "     |      7.1      |Tension | Fair.
+  lattice       |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  main girders, |47.0 |Flange   | 10.0  |   ..  |Compres-| Fair.
+  plate         |     |edge     |       |       |sion    |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|26.0 |Flange   |   ..  |  6.7  |Tension | Fair.
+  plate         |     |         |       |       |        |
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|11.0 |   "     |  6.3  |  6.5  |   "    | Bad; loose
+  plate         |     |         |       |       |        | rivets.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|19.0 |   "     |  8.4  |  9.1  |   "    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Wrought-iron  |     |         |       |       |        |
+  cross-girders,|22.0 |   "     | 10.5  | 11.1  |   "    | Good, but
+  plate         |     |         |       |       |        | rusted.
+                |     |         |       |       |        |
+  Steel trough  |    {|   "     |     15.0      |   "    |}Fair,
+  girder        |15.7{|Top edge |     32.0      |Compres-|}but
+                |    {|         |       |       |sion    |}rusted.
+                |     |         |       |       |        |
+  Steel         |18.7 |Flanges  |  7.5  |   ..  |Tension | Fair,
+  troughing     |     |         |       |       |and Com-| but
+                |     |         |       |       |pression| rusted.
+  --------------+-----+---------+-------+-------+--------+-----------
+
+It would be unwise to infer from the instances which have been quoted
+that high stress may be regarded with complaisance. In the most
+conscientious engineering work there should still be a liberal margin
+for material possibly defective, or even bad, for waste and
+deterioration, and for the aggregate effect of minor errors in design,
+any one of which considerations, except the first, by itself might not
+be of great importance. The conclusion which may, however, be derived
+from this and the previous chapters is, that bridge failures are less
+likely to occur from high stress of a kind readily calculated than from
+failure in detail, obscure and little suspected, the reason for which is
+not perhaps apparent, till the attention is forcibly directed to it by
+the refusal of the structure to sustain the forces to which it may be
+liable.
+
+
+
+
+CHAPTER VII.
+
+DEFORMATIONS.
+
+
+Instructive lessons are to be had from a study of the various
+alterations in form to which metallic bridgework is liable, which
+alterations may be due simply to the development of stress of ordinary
+amount, and are then generally small; or to abnormal stresses, the
+result of some distortion in the bridge structure itself not originally
+intended, and possibly extreme. In addition to these there may be
+deformations due to settlement, to "creeping" of parts of the structure
+relative to the rest, to temperature changes, to rust, and to original
+bad workmanship. In any instance quoted below the methods adopted to
+ascertain the amounts of such alterations were quite simple, even crude;
+but as care was exercised, and no attempt made to measure any very
+minute changes, the results may be accepted as practically correct.
+
+Dismissing for the present changes of form such as are to be expected,
+and touched upon in other places in this work, with respect to the
+particular parts of bridge structures affected by them, a few instances
+will be adduced of alterations which, though not very surprising, are
+such as in the design of the work are hardly likely, in most instances,
+to have been contemplated.
+
+A case has already been referred to in which, owing to eccentric loading
+of main girders, these were, as to the top flanges, flexed sideways a
+considerable amount. It is proposed to supplement this by further
+remarks relative to somewhat similar cases. A like effect is frequently
+to be observed in trough or twin girders, in which the rails are
+supported upon longitudinal timbers resting upon projecting ledges
+formed by the bottom angle-bars of such troughs. In old forms of this
+arrangement it is common to find the two girders forming the trough
+connected only by bolts passing through the timbers, or just above them
+and below the rails; or connected by narrow strips, which serve no other
+purpose than to prevent the sides spreading at the bottom. The top
+flanges in such cases commonly curve inwards on the passage of the
+running load, accompanied of necessity by an increase of compressive
+stress upon the outer edges of the flanges, and perhaps by the working
+of any flange-joint which may exist. This, both as to flexing of the top
+flange and the working of a joint, was noticed in the case of a bridge
+twenty-three years old, very similar to that illustrated in Figs. 8 and
+9, and described on pages 13 and 14. The top flange consisted, however,
+of a bridge rail riveted to the top edge of the web, butting at a joint,
+and covered by thick cover strips (see Fig. 48). The joint itself was
+poor, and depended largely upon the character of the butt, which was not
+sufficiently good to prevent the top member kinking at this point, under
+the joint influence of transverse effort and compressive stress, with
+possibly some help from bolts passing through timber and webs, though
+these being loose, the author does not think them at all responsible.
+Although not strictly relevant, it may be remarked in passing that it is
+very objectionable to use bolts as was done in this instance; for as the
+timber settles down on its seat, taking the bolts with it, these bear
+hard in the webs, enlarging or even, as in this case, tearing the holes,
+accompanied by injury to the bolts themselves. The practice is now
+almost obsolete, but the example is instructive as showing the
+impropriety of securing timbers by bolts passing through them at right
+angles to the action of the load, unless these bolts are quite free to
+move with the timber as it compresses.
+
+If trough girders must be used, the better plan is to connect the two
+sides by a continuous bottom plate, the trough thus formed being
+properly drained, if the timber is not bedded in asphalt concrete; or to
+introduce stiff diaphragms at intervals beneath timbers, if the depth
+suffices.
+
+In the case just quoted the curvature of the top members of the girders
+was inwards, but in the instance given below, of twin girders 26 feet
+effective span, with longitudinal timbers between, resting, as before,
+upon the inner ledge formed by the bottom flanges, the curvature was
+observed in three out of four girders to be 1/2 inch in a contrary
+direction, the fourth remaining straight.
+
+[Illustration: FIG. 48.]
+
+[Illustration: FIG. 49.]
+
+An inspection of the accompanying section, Fig. 49, will, perhaps,
+render the reason evident when it is noticed that the top members are
+very unsymmetrical in form, the effect of this being to give these
+members, under stress, a strong tendency to flex outwards, apparently
+more than sufficient to counteract the tendency of an eccentric
+application of load on the bottom flange to bring them inwards. It is to
+be observed that the eccentricity of the flange appears to be not
+materially in excess, and is actually so, only because the thinness of
+the web--1/4 inch--renders it incompetent to keep the bottom flange up
+to its work, and so secure the full effect of the eccentric loading in
+limiting the outward tendency, due to the section of the top member,
+the effects of which are thus more apparent than would have been the
+case with a stiffer web. Ties across from one bottom flange to the other
+prevent the want of symmetry noticed in these--which, by the way, is on
+the wrong side for utility--from having any particular effect.
+
+To give one other example of the consequences of eccentric loading, a
+bridge of 48 feet effective span may be quoted. This bridge carried four
+lines of way supported by five main girders, trussed by kicking-struts
+in such a manner as to form a bastard arch. A part section and plan are
+given in Figs. 50 and 51.
+
+[Illustration: FIG. 50.]
+
+[Illustration: FIG. 51.]
+
+The floor consisted of Lindsay's troughing resting upon the lower
+flanges of the main girders, the three middle girders, subject to
+eccentric loading, sometimes on one side, sometimes on the other, were,
+with dead load only, straight; but the two outer girders, liable to
+loading only on one side, had, under repeated applications of such a
+load, assumed a permanent curve towards the rails--13/16 inch in one
+case and 1 inch in the other--which curvature, no doubt, increased when
+a live load came upon the contiguous roads, though this was not
+measured. It should be remarked in passing that, owing to settlement and
+the canting of the abutments, the three middle girders were also
+"down"--in one case 3/4 inch. The girders, with one near road loaded,
+deflected 1/8 inch--greatly less than would have been the case had the
+main girder not been trussed. The bridge, at the time these particulars
+were obtained, had been in existence six years.
+
+Deformations due to settlement may be very considerable. The author
+recalls two instances affecting continuous girders. In the first of
+these, a bridge twenty years old, of two spans of about 50 feet each,
+and with girders 4 feet 6 inches deep, the centre pier had sunk 4
+inches, reducing the spans, as respects the dead load, practically to
+the condition of simple beams, just resting, but hardly bearing, upon
+the piers when free of live load.
+
+In the second case, also of two openings of about 55 feet each, with
+girders 8 feet deep, one abutment had sunk about 3 inches, more than
+doubling the stresses over the centre pier. It is manifest that
+continuous girders should only be adopted where settlement of the
+supporting points is not likely to occur to any material degree. If this
+cannot be relied upon, the theoretical flange sections may hardly be
+worked to with any prudence; it being then advisable to make a liberal
+allowance for settlement stresses, in which case any economical
+advantage that should exist will probably disappear. It is, however, to
+be acknowledged that so long as the girders are in touch, under dead
+load, with the bearings intended to support them, the stresses due to a
+live load are unaltered, the principal effect in this case being that
+the variation in stress due to the live load ranges between limits that
+are higher or lower in the scale of stress than is the case with
+bearings undisturbed; still, if it is desired that the maximum stress
+shall not exceed, say, 6 tons per square inch, it can hardly be a matter
+of indifference that settlement shall induce a maximum of, perhaps, 10
+tons, as in that case the stress must be 4 tons nearer the limit of
+statical strength.
+
+Before leaving this matter it may be well to point out that in the case
+of continuous girders of uniform section a moderate settlement of the
+piers may even be advantageous by reducing the moments over the piers,
+and possibly making them equal to those obtaining near the middle of the
+spans, in which case there will be less inequality of stress in the
+booms and a reduction of the maximum stress.
+
+Bridges consisting of simple main girders connected by cross-girders may
+be very prejudicially affected by unequal settlement; for instance, if
+one girder bearing settles more than the others, a twist is put upon the
+structure very trying to the floor-girder connections, and possibly to
+the main girders; to the web if a plate girder, or to the verticals if
+an open-webbed truss with rigid cross-girder attachments. Indeed,
+settlement of this kind may be much more destructive to a metallic
+bridge than to an arch of brick or masonry, the commonly accepted
+opinion notwithstanding.
+
+Instances of deformations due to the creeping of some part of the
+structure away from its work, are within the author's knowledge, rare;
+except in the case of the ends of main girders in skew bridges, already
+referred to.
+
+Distortion, the result of temperature changes, is frequently to be
+observed in any considerable length of girder flange or parapet where
+there is not freedom of movement, unless due provision is made to check
+it.
+
+It is quite common to see parapets out of line, either because the ends
+are not free, or because the light work of the parapet being more
+exposed to the sun's rays than the girder work to which the lower part
+is attached, expanding to a greater degree, is subject to considerable
+compressive force, and buckles under its influence. The cure for this
+condition is obviously to provide such parapets with free or flexible
+joints at moderate distances apart, or to make the parapet sufficiently
+stiff to take the stresses developed, without crippling. A parapet may
+also go out of shape if directly attached to the top flange of a girder
+liable to heavy loading, particularly if the girder be shallower than
+the parapet, simply by its inability to maintain truth of line under the
+compressive stress, which it shares with the top flange of the girder
+proper.
+
+Rivets spaced too far apart, by allowing the plates or other parts to
+spring open slightly, and permitting moisture to enter, results in the
+growth of rust, which, as it swells in forming, forces the parts
+asunder, and may set up considerable stress.
+
+Flat bars riveted together by rivets spaced 12 inches apart may from
+this cause be forced asunder, as much as 1/2 inch, sufficient to set up
+a stress, with any practicable thickness of bar, much exceeding the
+elastic limit.
+
+Local distortions may occur as the result of imperfect workmanship or
+careless erection, causing quite possibly very severe local stresses; or
+girder flanges may be out of straight as a result of riveting up along
+one side first, instead of advancing the riveting simultaneously along
+the whole breadth of the flange. The injury done by drifting is well
+known, and there is reason to think considerable damage is sometimes
+done to girderwork during manufacture by rough treatment to make the
+work come together; but the author has little to offer with respect to
+these matters that is not common knowledge. It may, however, be pointed
+out in passing that a bridge upon the design of which great care has
+been expended, with the idea that theoretical propriety shall not be
+violated, may be completely spoiled in this respect by careless
+construction. Fortunately, both steel and wrought iron, if of good
+quality, are long suffering. Incompetent erection will sometimes result
+in the true girder camber not appearing, or in differences as between
+girders supposed to be similar. This is not, of course, a deformation in
+the sense in which the word has previously been used, but it is
+desirable to bear the fact in mind as a possible cause of defective
+camber in dealing with questions of deformation.
+
+The foregoing has reference chiefly to alterations of form in bridgework
+of wrought iron or steel, but a case of considerable interest is that of
+a cast-iron arched structure, of which the author made a very complete
+examination.
+
+[Illustration: FIG. 52.]
+
+[Illustration: FIG. 53.]
+
+This bridge, built in 1839, and carrying two lines of railway, consisted
+of three spans, 100 feet each, of 10 feet rise, made up of four inner
+and two outer ribs, each rib being in three nearly equal parts; the
+floor was of timber, the abutments and piers of masonry. As originally
+constructed there was no bracing between the ribs other than the frames
+indicated on the plan here given (Fig. 52), stretching from outer rib
+to outer rib in the neighbourhood of the rib joints, which were simple
+butts without bolts or any equivalent means of connection. The floor
+was, however, braced in the horizontal plane, and the structure was also
+braced over the masonry piers. After forty-two years' use supplementary
+distance-pieces were introduced between the ribs, but still no bracing
+between them, or any efficient means of checking lateral movement. A
+crack developing in one of the outer ribs at the crown, led to an
+investigation to trace the cause, the bridge then being fifty-four years
+old. Careful plumbing of the abutments revealed the fact that three out
+of four abutment pilasters were out of the vertical, as shown in Figs.
+52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner
+from which the cracked rib had its springing; there was also other
+evidence of settlement in an old crack extending from the top of the
+abutment to the ground level, although this movement was very old,
+certainly as to the greater part. The ribs of this span were also out of
+plumb, that which was cracked being 2-1/2 inches out at the centre. The
+joints of the ribs, which, as already stated, were simple butts, in some
+cases opened and shut, as the load passed over, in such a way as to
+suggest that the ribs were acting, in a manner, as four-hinged arches,
+of which two hinges were at the springing, and the other two at the
+joints, one of which would for most positions of the load be out of use,
+reducing the rib to the three-hinged condition; in other words, as the
+rolling load passed over the span, one or other of the two joints of a
+rib would "gape" an appreciable amount at the bottom or at the top.
+Observations were taken by means of a theodolite placed below, either
+upon the bank or upon the tops of the masonry piers, sighting upon
+suitable scales attached to the ribs to ascertain the amounts of
+vertical and horizontal movement during the passage of trains over the
+bridge. The principal results are set forth in the following table:--
+
+MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT.
+SPANS.
+
+  ----------------------+-------+----------+-----------
+                        |Fall in| Rise in  | Lateral
+            --          |Inches.| Inches.  | Movement
+                        |       |          |in Inches.
+  ----------------------+-------+----------+-----------
+                      _Span No. 1._
+  At A. Up road loaded  |  .20  |   .08    |   .04
+   " A. Down road loaded|  .08  |   .03    |   .04
+   " B. Down road loaded|  .14  |No record.|   .02
+                      _Span No. 2._
+  At C. Up road loaded  |  .40  |   .13    |  Slight.
+   " C. Down road loaded|  .10  |   .05    |     "
+                      _Span No. 3._
+  At D. Up road loaded  |  .22  |No record.| No record.
+   " D. Down road loaded|  .15  | Slight.  |  Slight.
+  ----------------------+-------+----------+-----------
+
+  NOTE.--The lateral movements are to either side of the mean position.
+
+The particulars for spans 2 and 3 were obtained with the instrument set
+up on the pier between these spans. The tremor of this pier was such
+that no useful readings for lateral movement could be obtained. Further,
+as the rolling load came upon these spans, the effect was to rock the
+pier to an extent vitiating the readings for vertical displacement; but
+by sighting upon the fixed abutment, and observing the amount of this
+rocking, suitable corrections were made in the apparent rib movements.
+The figures given in the table are thus corrected. The pier rocking was
+equivalent, as an extreme, to an inclination from the vertical of 1 in
+3200. An attempt to measure the horizontal movement of the pier-top was
+unsuccessful, owing to the impracticability of setting up the instrument
+in a suitable position, sufficiently near to the pier to enable readings
+to be satisfactorily taken. This horizontal displacement probably
+amounted to about 1/16 inch either way. The rise and fall of the arches,
+and rocking either way of the piers, varied, as might be expected, in
+accordance with the position of the running load with respect to the
+spans. Summarising the results, the greatest vertical movements
+downwards were 0.20 inch, 0.40 inch, and 0.22 inch for spans Nos. 1, 2,
+and 3, the upward movements being 0.08 inch and 0.13 inch for the first
+and second spans, there being no recorded result of this kind for the
+third span. With adjacent ribs loaded, the movement of the ribs unloaded
+was one from one-third to one-half of the full amounts. It is to be
+noted that the lateral displacement in no case exceeded 0.04 inch either
+way, nor were the vertical movements exceptional; yet, as a matter of
+sensation, when seated upon the ironwork, it was a little difficult to
+believe them really so moderate. Observations were also made to
+ascertain the rise of the arches from winter to summer temperatures,
+with the result that this was found to be 0.45 inch, 0.45 inch, and 0.55
+inch for the spans in order, the extreme temperatures being fairly
+representative of the English winter and summer. The structure was, as a
+consequence of the examination, efficiently braced by diaphragms between
+the ribs, and diagonals following the arch ribs round from springing to
+springing, with satisfactory results. The crack already referred to, and
+its probable causes, will be dealt with under "Cast-Iron Bridges."
+Eventually this bridge was reconstructed to meet the requirements of
+growing engine-loads.
+
+
+
+
+CHAPTER VIII.
+
+DEFLECTIONS.
+
+
+Deflection, considered only as a fraction of the span, and without
+regard to other conditions affecting it, is of very little use as an
+indication of a girder's fitness for its work; but when taken with
+reference to the depth of the girder, the nature and amount of the load
+producing flexure, and, further, with regard to the quality of the
+workmanship and normal properties of the material of which the beam is
+constructed, it may be of some little service in helping to form a
+reliable opinion. This consideration applies with less force, perhaps,
+to new work than to old, in which there may be unknown influences at
+work, or unknown defects which by excessive deflection may be betrayed.
+Though too much importance should not be attached to results of
+deflection tests in any one instance, yet the practice of observing such
+movements, and considering them with reference to each case, gives a
+good general idea of what may be expected in a fresh instance, any
+material departure from which should be a reason for specific inquiry as
+to the cause. A further reason with new work is found in the evidence it
+affords as to whether the loads carried travel to the supports really as
+intended, or by some route not contemplated; or, in the case of floor
+beams, in what way the load is distributed amongst them, if, indeed,
+there be any such distribution.
+
+The author has commonly found that new work gives greater deflections
+than old--i.e., while calculation gives the same result for each, it
+does not apply equally well to both. The differences may be accidental,
+but are probably due to other causes, perhaps to the fact that new work
+has not by repeated applications of load lost the resilience of parts
+liable to considerable local stress, such as is very liable to occur at
+connections, so that the deflection is, whilst new, greater than after
+many years' use, by which time such parts may develop a definite "set,"
+and contribute in a less degree, or not at all, to the total elastic
+deformation.
+
+It is also possible, as already suggested, that repeated high stress may
+reduce the ratio of strain to stress, the material gradually becoming
+more rigid, the modulus of elasticity being, in fact, increased.
+
+In girders of ordinary construction, the major part of the deflection is
+due to the booms, the remainder to the web; the latter is for plate
+girders a small amount only, and is commonly neglected, but for open web
+constructions it may be quite appreciable. For any given type of web
+arrangement the deflection due to the web will, for all depths, remain a
+constant quantity for the same span and unit stress; and though a
+moderate fraction of the whole deflection for a shallow girder, it may
+be a very considerable part for a girder of great depth, in which that
+part due to the booms is, of course, smaller, since the deflection due
+to these varies inversely as the girders' depths.
+
+Deflection, being dependent upon the elasticity of the material, is of
+necessity very largely influenced by the value of its modulus E, itself
+liable to considerable variation, and is increased in a small degree by
+the yield of joints and rivets, which effect, apart from the initial
+"set" of the girders, appears to be negligible. The stiffness of members
+in resisting angular distortion at connections must also, for open-web
+riveted structures, affect the result, making it somewhat less, and,
+finally, section excess at joints and gusset attachments has an
+influence in modifying deflection as compared with that due to the
+normal gross sections simply.
+
+From these considerations it is apparent that any simple deflection
+formula must be largely empiric in its nature. For plate girders of
+uniform depth and flange stress, the writer has found the following to
+give good results:--
+
+    S squared
+  ----- x _f_ = deflection in inches.
+  D x C
+
+The span S and depth D are, as a matter of convenience, taken in feet;
+the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is
+the mean of the extreme tensile and compressive stresses of the booms,
+in tons per square inch, estimated upon the gross sections.
+
+This, though satisfactory for plate girders, is not so suited to girders
+having open webs, in which the deflection will more nearly be
+
+  (3S     S squared )
+  (-- + -----) x _f_,
+  (C    D x C)
+
+the constant C being 3900 and 4450 for iron and steel respectively. The
+latter values of C correspond to normal values of the modulus of
+elasticity of 11,700 and 13,350 tons for iron and for steel, it being
+assumed that any slight rivet yield is off-set by any small section
+excess--say, 5 per cent.; it may, however, happen that section excess is
+greater than assumed, in which case some allowance may properly be made
+for this by increasing C.
+
+To adapt the formulae to girders other than those having parallel booms
+and uniform stress, the results, as deduced above, may be multiplied by
+constants given in column B of the Table given on page 93.
+
+The practice of adopting for E in deflection formulae a quantity much
+smaller than its nominal amount, with the object of allowing in riveted
+girder work for the yield of rivets and of joints, can hardly now be
+defended, whatever may have been a case at a time when workmanship was
+much inferior, when there was no machine riveting, and joints were,
+owing to the small weight of plates and bars, three times as numerous.
+
+The initial "set" of a girder consequent upon first loading is a
+quantity quite distinct from deflection proper, and may be so small as
+to be negligible, or read 10 per cent. of the true deflection, varying
+with design and workmanship.
+
+No estimate of girder deflection can be even approximately true if there
+is, at the level of the top or bottom flanges, a plated or otherwise
+rigid floor system which is not taken into account, as this will have
+the effect of very materially reducing the boom stress. To neglect this
+influence, where it exists, must necessarily lead to disappointing
+results, and it is quite practicable in many instances to include it in
+the calculation.
+
+The influence of angular distortion between the various members has been
+neglected. It may be pointed out, however, that the resistance
+accompanying these movements in girders having riveted connections,
+though unimportant as affecting deflection, is worth some consideration
+in regard to secondary stress. For girders of similar type and unit
+stress these angular variations will be the same in amount for any span,
+but will generally be of less importance in large girders than in small,
+because in large girders the ratio of the breadth of members to their
+length is commonly less.
+
+When determining the probable deflection of any girder of exceptional
+figure, it will be found convenient to make a strain diagram--an old
+device, in which the actual alterations of length being ascertained for
+all members, the girder is carefully set out to a suitable scale, with
+the lengths of members increased or reduced by the actual estimated
+amounts. The distorted figure resulting will then give the probable
+deflection. The value of E for this purpose should never be taken at
+less than the normal amount, and may for a considerable excess of metal
+in joints and gussets be made as much as 10 per cent. greater, this
+being a convenient means of making the necessary correction.
+
+The effect of loads quickly applied may here be considered in connection
+with elastic deformations of girders of the same span, but different
+depths. If these be designed for similar loads and unit stresses, the
+deflections due to webs and booms of the girders compared will bear the
+same relation, each to each, as do the weights, whether in both cases
+the loads be inert or quickly applied, from which it follows that the
+mechanical "work" done by the loads in falling through the deflection
+heights is, neglecting inertia, always in proportion to the girderwork
+weights, and is a similar amount per ton, which as the total length of
+members remains substantially unaltered, corresponds to a similar amount
+of work per unit of section, or similar stress, irrespective of the
+depth of the girders.
+
+But for a "drop" load, as when there is some obstruction upon a railway
+bridge, there will be in addition a further amount of work to be
+absorbed, which is to be considered the same whatever the girder's
+depth, and will for deep girders be a larger amount per ton of
+girderwork than in those that are shallow; this, taking effect on
+members of the same aggregate length, but lighter, will develop a higher
+stress than in girders of lesser depth, more particularly in the booms.
+
+The influence of the girder's inertia in modifying drop-load effects
+will also be less marked in deep--i.e., light--girders than in girders
+shallow and heavy.
+
+It is, notwithstanding all this, desirable that the depth of main
+girders should be liberal for economy's sake, and also that of floor
+beams, for reasons already dealt with; the probability of the drop load
+is somewhat remote, and, though possible, would simply induce, if it
+occurred, an increment of stress rather more important in deep girders,
+making it specially desirable in these to give particular attention to
+the detailing of any connections liable to suffer from impact effects.
+
+It should be remarked that for short and very flexible beams, generally
+outside the limits of practice, there may also be, under quickly moving
+loads, a material increase of stress due to the centrifugal effort of
+the load on running round the deflection curve, and in rising upon the
+steep part of the curve beyond the girder's centre. Where advisable,
+these effects may be modified by cambering the rail.
+
+For pin bridges in which there may be spring in the pins, excess stress
+in some eye-bars due to inequalities of length, and a want of that
+rigidity peculiar to riveted structures, the deflection will be greater
+than above indicated for girders of the ordinary English type.
+
+The method in common use for measuring the deflections of girders but a
+moderate distance above the ground by means of sliding-rods, though
+crude, gives, with care, results sufficiently accurate for most
+practical purposes; but some points necessary to remember may be
+mentioned with propriety. The lower rod should rest firmly upon
+something solid, say a stone, well bedded and free from any tendency to
+rock; the upper end should bear against some part of the girder above,
+presenting a hard surface, free from dirt or scale, and as the running
+load approaches the bridge it should be ascertained that there is no
+slack, that the rods bear hard at the top and bottom. The upper end
+having been depressed, care is to be exercised to make sure of the
+reading before the rods alter their relation to each other. These
+precautions are so self-evident that an apology is almost necessary for
+mentioning them.
+
+To ascertain deflections with a single pair of rods is only allowable
+when the girders rest firmly on their bearings; if felt has been placed
+under the girder ends, or if the bedstones are insecure or rocking, it
+is necessary to use three pairs of rods, one pair at the middle and a
+pair at each end, in which case the mean of the two end readings must be
+deducted from the reading of that at the centre to get the desired
+result.
+
+In the case of a number of spans in series, each resting upon sill
+girders common to two sets of bearings, this method also gives results
+of indifferent reliability, as the depression of each end may be greater
+as the travelling load comes upon and leaves the span than when it is
+precisely over the middle, and it is in general out of the question to
+secure by this mode simultaneous readings for a particular position of
+the running load, which are what is required.
+
+The author suggests, as a means of ascertaining deflections free from
+these objections, that it should be done by first measuring the slope at
+one end, and from this deducing the deflection at the centre.
+
+This is to be accomplished by means of a little instrument, consisting
+of a telescope with cross-hair sights, and fitted with a reflecting
+prism at the eye-piece capable of being turned round, so that the
+observer has a wide choice as to the position he assumes with reference
+to the instrument, and may look either directly through it, or at right
+angles to the axis of the telescope. This is clamped at one end of the
+girder over the bearing, at the other end a scale is secured, to which
+the telescope is directed, the cross hair being made to sight on the
+zero of the scale, or the reading noted. For a girder supposed to
+deflect to uniform curvature (say, with uniform depth and uniform
+stress, the ordinary case) the reading observed will be four times the
+deflection; every 1/10 inch actual reading on the scale will correspond
+to 1/40 inch of girder deflection.
+
+Apart from the deflection, this method gives a ready means of observing
+the end slope, a quantity of equal value for purposes of comparison. As
+with girders of similar proportions, and similarly stressed, the
+deflection will at all spans be the same fraction of the span; so should
+the end slope be a constant quantity under similar conditions, the
+diagram, Fig. 54, will make the principle quite clear.
+
+[Illustration: FIGS. 54 to 57.]
+
+Strictly the character of the deflection curve is slightly modified by
+that part of the deflection due to the web; so that the depression at
+the centre would, in the case assumed above, be somewhat more than
+one-fourth part of the end reading, and generally will be a larger
+fraction of the reading than that deduced from a consideration of flange
+stress simply. In Figs. 55 to 57, which are intended to explain this,
+it will be noticed that deflection due to the web is shown
+straight-lined from the bearings to the centre of the girder; this is
+strictly true only for a girder correctly designed for an immovable
+distributed load; but as there should be for girders intended for a
+travelling load, some excess in web members near the centre under the
+condition of uniform loading, the point of the figure should be rounded
+off to be in agreement with this case, though it is left as shown in the
+diagram for the sake of simplicity.
+
+Suitable constants, including the corrections necessary, are given in
+column A of the table annexed for a few typical cases, and by these
+constants the actual readings should be multiplied to find the
+deflection. The constants have been worked out for depths of one-tenth
+the span; for greater depths they should be slightly more, and for
+smaller depths somewhat less, but they may be used between the limits of
+one-sixth and one-fourteenth, with a maximum error hardly exceeding 5
+per cent., and generally much less.
+
+The figures in column B relate to the formulae previously stated, and
+apply equally well to all depths.
+
+TABLES OF MULTIPLIERS FOR DEFLECTION.
+
+  _Uniform Stress_:                                           A.     B.
+      Girders of uniform depth, varying flange section       0.27   1.00
+      Hog-backed girders, ends half of centre depth, varying
+      flange section                                         0.24   1.08
+  _Varying Stress_:
+      [1]Girders of uniform depth and flange section         0.32   0.87
+      [1]Hog-backed girders (as above), but uniform flange
+      section                                                0.29   0.97
+      [1]Bow-string girders of uniform flange section        0.16   1.30
+
+[1] For uniform loading.
+
+It is apparent that, if preferred, the scale, instead of being in
+inches, divided suitably, may, for each type of girder, be amplified to
+the proper degree, so that the amount of the deflection may be read off
+at once.
+
+This method of dealing with deflections is quite independent of the
+character of the bearings, and is applicable to girders at any height
+above ground or over water; but its use would hardly be practicable for
+very small beams, or those in an awkward position, or near which it
+would be impossible to remain with a running load upon the bridge.
+
+There is a possible source of error in the use of the instrument, most
+likely to occur with triangulated girders, with which, if the instrument
+is placed at the top of an end post, the reading observed may be the
+joint effect of deflection and of local flexure of the members meeting
+near the telescope. This may be tested, and, if necessary, allowed for,
+by first sighting upon a scale at the next apex, and observing the
+effect of the moving load. Again, as girders sometimes cant towards the
+running load, if the instrument is placed on one edge of a girder, and
+the cantings of the two ends are dissimilar, a false reading will
+result, which may be amended by ascertaining the amount of cant at each
+end, and correcting for the effect of the difference between the cants
+upon the observation. Only in exceptional cases is it likely that either
+of these considerations would need attention.
+
+The author has secured with this instrument very promising results,
+notwithstanding that under a running load there is a slight haziness of
+the scale as seen through the telescope, due to "dither," largely the
+result of imperfections which may be remedied.
+
+Deflections may sometimes be conveniently taken, by a quick-eyed
+observer, with a good surveyor's level and a specially-divided staff
+held at the centre of the girder. The divisions preferred by the author
+for this purpose are 1/10 inch, plainly marked, which may be seen at 50
+feet distance with sufficient clearness to make possible readings by
+estimation between the divisions to, say, 1/50 inch. But it is clearly
+desirable not to rely upon a single observation only, where all the
+evidence is gone so soon as the sight has been taken.
+
+In rail-bearers, or other short girders, it may not be practicable to
+adopt such methods, either on account of an inability to find a suitable
+place for the instrument, or to read with any telescope with sufficient
+promptitude as the load passes rapidly over. The use of rods may also be
+out of the question, as the errors attending their manipulation may be
+serious where but a small movement has to be noted, this being
+complicated in some instances by the bearings being insecure, and
+working to an extent which obscures the measurement sought. In such
+cases it is preferable to use a stiff slat lying along the girder, which
+bears, through short blocks over the girder bearings, upon the flanges;
+the deflection is then read by direct measurement of the girder's
+depression at the centre, relative to the slat.
+
+The author is, unfortunately, not able to give any precise information
+on the effect of running-load as against a load that is stationary in
+connection with girder deflections. It is by no means easy in ordinary
+work upon a railway to secure facilities for making such comparative
+tests. It may, however, be confidently stated, as a result of such
+observations as he has made, that the deflection due to a load coming
+rapidly upon a bridge is, as to the main girders of, say, a 50 feet
+span, but little greater than that due to the same load stationary; it
+may be, perhaps, 5 to 10 per cent. more.
+
+It is evident that to determine the precise difference where the
+quantity to be measured is so small needs apparatus of a more delicate
+character than that in common use, and the control of an engine, or
+engines, for the purpose of making the special tests, conditions which
+on a busy line can only be secured by special arrangements previously
+made.
+
+
+
+
+CHAPTER IX.
+
+DECAY AND PAINTING.
+
+
+The author has collected particulars as to the amount and rate of
+rusting in metallic structures which are of some interest. In all such
+instances it is very necessary to note the conditions which have
+obtained during the process of wasting, as without this, misleading
+conclusions may be drawn. The information given relates in all cases to
+wrought iron, unless otherwise stated.
+
+A plate-girder bridge, having girders under rails, was found to be badly
+rusted. The atmospheric conditions were unusually trying, the air being
+damp and impregnated with acid fumes from adjacent steel works. That the
+wasting was largely due to this latter cause was indicated by the fact
+that the girders nearest to the steel works suffered more than those
+farther removed and partly sheltered from the corrosive influence.
+
+The webs were in places eaten right through, having lost a mean amount
+of about 1/8 inch full on each surface in twenty-eight years. Painting
+had not been well attended to.
+
+In a similar bridge, not a great distance from this, but sufficiently
+far away to modify the conditions for the better, considerable wasting
+was also observed, but more particularly where the girders had been
+built into masonry, which, loosening with the constant movement of the
+girder-ends, had allowed moisture to collect, and rust to develop,
+without the chance of repainting these surfaces. The amount of waste at
+the places indicated was, as in the last case, about 1/8 inch on each
+face, and in the same time, other parts of the girders having suffered
+less.
+
+[Illustration: FIG. 58.]
+
+A third plate-girder bridge, with outer main girders, cross-girders, and
+plated floor, carrying a road over a railway and sidings, and which was
+known to have been neglected in the matter of painting, was very badly
+rusted, both as to the cross-girders and floor-plates. The atmosphere
+was somewhat damp; the chief cause of deterioration was, however, the
+smoke and steam from locomotives, which frequently stood for some time,
+during shunting operations, directly under the bridge. The webs of the
+cross-girders, which were originally 1/4 inch thick, had rusted into
+occasional holes during fourteen years--i.e. 1/8 inch from each surface
+in that time. When removed a little later the wasting was so complete
+that it was possible to knock out with a light hammer the remains of the
+web between flanges and stiffeners, so as to leave an open frame only.
+One of the cross-girders was so treated by the men engaged upon the
+work, when it presented the appearance shown in Fig. 58.
+
+In another case--that of a bridge with lattice girders under rails--the
+ends were built into masonry, which had, of course, loosened, with the
+usual result. The air of the locality was certainly pure, but somewhat
+damp. The general condition of the ironwork was good, but end-bars of
+the diagonal bracing, where they had been closed in, had lost 1/8 inch
+on each surface in thirty-three years. The top flanges immediately under
+the timber floor were in a very fair state, which is of some interest
+when it is considered that these were made of steel of the same kind as
+that already noticed as being used in the construction of small girders
+(see Fig. 46, _ante_), described in the chapter upon "High Stress," both
+cases dating from the year 1861. The painting upon the lattice-girder
+bridge had been pretty well attended to; but in the case of the small
+steel girders it had been greatly--perhaps altogether--neglected; this,
+coupled with adverse atmospheric conditions, had produced the result
+that the rate of rusting had for the small girders been much greater
+than that of the steel top flange referred to, being fully 1/8 inch on
+each surface, as against a negligible amount under the more favourable
+circumstances.
+
+Girder-work over sea-water, as in piers, seems to rust at a sensibly
+greater rate than inland work under average conditions; but it is hardly
+practicable to make any strict comparison, as in either case the rate of
+oxidation is so much affected--even controlled--by the care bestowed
+upon the structures. This general conclusion is based upon the results
+of examination of wrought-iron girder-work over sea-water of ages
+varying from fourteen to forty-four years. It should be remarked,
+however, that in one case steel girders but five years old, and which
+were frequently wetted with sea-spray, were found to be wasting rather
+badly--the paint refusing to keep upon the surface.
+
+It may be concluded from the above instances, and from others which have
+come under notice, that wrought-iron work, if not properly cared for in
+respect to painting, or under conditions otherwise bad, may be expected
+to rust at a rate which corresponds to the loss of 1/8 inch on each
+surface in from fifteen to thirty years; but with proper care as to
+painting, and exclusive of exceptionally bad conditions, it does not
+appear to waste at any measurable rate. In some instances, upon scraping
+the paint from girders which had been in use for thirty years, the
+author has found, beneath the original red lead, the metallic surface
+bright and clean, showing no trace of rust.
+
+Of ordinary steelwork the same cannot be said, the common experience
+being that mild steel is very liable to be attacked by rust. With
+passable care in the bridge-yard during manufacture, such that with
+wrought iron no after-trouble would be noticeable, steel is very liable
+to show, within a year of being built up, numerous little blisters on
+the painted surface; any one of these being broken away discloses a
+small rust-pit. This is more often seen on the flange surfaces
+(horizontal) than on web surfaces (vertical), but it is probable the
+position has little to do with the matter, and that it is rather due to
+the fact that rust has been earlier started on the flange-plates, upon
+being put through the drilling-machines and inundated with slurry, which
+occurs only to a more limited extent with webs having fewer holes. The
+heads of steel rivets do not show this tendency to "pit," or to early
+development of rust. The riveting is about the last operation in making
+a girder, each rivet being freed of all rust by heating, and quickly
+coming under the protection of oil or paint. It may happen in this way
+that the heads of rivets on a girder may be exposed without protection
+for as many hours only as the rest of the work for weeks, which fully
+accounts for the difference in behaviour.
+
+The essential point to be observed in all steelwork is to prevent, if
+possible, the first development of rust, for once begun it is much more
+difficult to arrest than in iron; for this reason, oiling of all
+material for a steel bridge, at a very early stage of its existence,
+cannot be too strongly insisted upon. This practice, however, makes the
+work so objectionable, and even dangerous when being lifted--because of
+the liability to slip--to the men engaged upon it, that it is commonly
+very difficult to ensure it being done sufficiently soon to satisfy a
+careful inspector. If the work is carried out under cover, the
+requirement is less urgent. Strictly, all material should be oiled so
+soon as rolled, but the author does not remember to have seen this done
+at any of the mills he has visited, though it is common enough to find
+it specified.
+
+Ironwork does not need the extreme care which should be bestowed upon
+steelwork, but it is desirable that it should be painted as soon as
+possible, the surfaces being first thoroughly cleaned.
+
+There is, probably, for painting girder work nothing to beat good red
+lead as a protective coating; but there is considerable difficulty in
+getting it reasonably pure, without which quality its utility will be
+greatly reduced. The question of purity will, however, be found to be
+largely a question of price. It may be stated broadly that, whether for
+steel or for iron, the first protective covering is, perhaps, the most
+important of any it will ever receive.
+
+In repainting old work, care should be taken to remove all traces of
+rust previous to laying on the new coat. It is not an altogether
+uncommon practice to repaint old structures by dealing only with the
+parts readily accessible, which, being less liable to rust, probably but
+little need it; leaving those parts which are difficult of access, and
+where rust is developing, untouched; treating the whole business as a
+matter of appearance simply. This, it need hardly be said, is
+indefensible. It is better rather to neglect the surfaces freely exposed
+and ventilated, and devote the whole care upon those other parts,
+confined and difficult to get at; taking the trouble necessary to remove
+ballast, timber, or whatever may obstruct the operation, in order that
+the bad places may be thoroughly scraped, and then painted. Those parts
+which most need attention may cost, perhaps, to reach--and deal with
+when exposed--ten times as much per yard of surface as the rest of the
+superfices, which needs little, and is always accessible; but the cost
+should not deter the proper carrying out of the work, as it will prove
+the very worst sort of economy to deal with painting in a perfunctory
+manner.
+
+It should be noted that girder work, whether of wrought or cast iron,
+when embedded in lime or cement concrete, or mortar, generally proves to
+be very well preserved, provided that close contact has obtained.
+Cast-iron girders, when carrying jack arches resting upon the bottom
+flanges, are found after long use to be in remarkably good order, when
+finally taken out, having, indeed, the surface appearance of new
+girders. Much the same remarks apply to girders of wrought iron carrying
+jack arches, where protected by the brickwork; provided that the girders
+are sufficiently stiff to minimise deflection, and allow the masonry or
+brickwork to adhere to the surfaces.
+
+Such girders are in a very different condition to those previously
+referred to, in which the ends of the girders, carrying a light floor
+structure, are built into masonry where the deflection slope is
+greatest; though, apart from the few cases where adherence can be relied
+upon, building-in is an undesirable practice, and has the disadvantage
+that after-examination is only possible by removing portions of the
+masonry, which it is evident would very seldom be resorted to.
+
+Cast iron has ordinarily--unlike wrought iron or steel--great capacity
+for resisting rust, and will, after many years of absolute neglect,
+appear but little the worse; an advantage which is the more pronounced
+when considered relatively to the greater thickness of the thinnest
+parts in cast-iron girders, the percentage of waste being
+proportionately lessened.
+
+Cast iron does, however, behave somewhat badly in sea-water, the metal
+sometimes losing its original character, and becoming in time quite
+soft; though, if not worn away, as by the attrition of shingle,
+maintaining its original bulk.
+
+Of some forty-five cast-iron piles belonging to various structures,
+examined whilst engaged upon sea-pier work for Mr. St. George-Moore,
+though the author found somewhat diverse results, in no case did there
+appear to be any general softening of the whole thickness, but a
+distinct change for some definite distance inwards, generally to be
+decided without difficulty, beyond which the metal appeared to retain
+its original character. In all cases any material depth of softening was
+found close to the ground, this depth rapidly decreasing higher up,
+till, at a height of 5 feet, but little if any softening could be
+detected. At 2 feet above ground the softening was frequently but
+one-quarter of that at ground level. There was, too, often a
+considerable difference in the behaviour of different piles in the same
+structure under similar conditions; one pile being found to have only
+one-fourth part of the softening noticed in others, or possibly none at
+all. For six different structures the amount of softening near ground
+level, of about twenty-five piles examined, was as given in the table on
+the next page.
+
+The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot
+above ground, in a pile thirty-six years old. The decayed material when
+removed was of a soft, greasy consistency, perfectly black, which a few
+hours later was found to have changed to a dry yellow powder, by the
+rapid absorption, it may be supposed, of atmospheric oxygen. It is
+apparent, therefore, from this example that deterioration may proceed to
+a considerable depth; but it should be observed that other piles of the
+set showed softening at ground level of 1/8 inch only.
+
+SOFTENING OF CAST-IRON PILES IN SEA-WATER.
+
+  ---+--------+----------+-----------+----------+---------+---------
+  No.|  Age.  | Maximum  |  Maximum  |Mean Rate | Quality |Materials
+     |        |Softening.|  Rate of  |    of    |of Metal.|Entered
+     |        |          |Softening. |Softening.|         |by Piles.
+  ---+--------+----------+-----------+----------+---------+---------
+  1  |17 years|5/16 in.  |1/8 in. in |1/8 in. in|Soft     |Extremely
+     |        |          |7 years    |15  years |         |soft
+     |        |          |           |          |         |sandstone.
+  2  |36 years|9/16  "   |1/8 in. in |No result |  "      |Rubble
+     |        |          |8-1/2 years|          |         |mound.
+  3  |32 years|3/8   "   |1/8 in. in |1/8 in. in|Moderate-|Fine
+     |        |          |11 years   |15  years |ly hard  |sand.
+  4  |38 years|1/10  "   |1/8 in. in |1/8 in. in|Hard     |Extremely
+     |        |          |47 years   |140 years |         |hard rock.
+  5  |17 years|Small     |Negligible |          |(?)      |Sand and
+     |        |          |           |          |         |Shingle.
+  6  |14 years|Negligible|Ditto      |          |(?)      |Sand.
+  ---+--------+----------+-----------+----------+---------+----------
+
+The least rate of softening noticed, apart from those structures of a
+more recent date, in two of which it was very slight, occurred in a
+pier thirty-eight years old (No. 4), where, of three piles tested, two
+were quite hard, and the third softened 1/10 inch only.
+
+Whatever may be the precise cause of the change, it does not appear to
+be affected by the period or percentage of immersion during the rise and
+fall of tides.
+
+[Illustration: FIG. 59.]
+
+This will be clear from the diagram, Fig. 59, which refers to four piles
+(No. 3 of table), all of the same age, in the same structure. On each
+pile the depth of softening is given at points in strict relation to
+each other, and to the tidal range. The percentages of immersion for the
+various heights are also given, from a study of which it will be
+apparent that these have no relation to the amount of softening; this,
+indeed, is always greatest near the ground, at whatever actual height it
+may be. For instance, pile A was at ground-level softened 1/4 inch,
+that point being 60 per cent. of its life under water; but on pile B, at
+a point 74 per cent. of the time submerged, and 4 feet above a lower
+ground-level, no softening was apparent; further, at ground-level of
+this pile, the percentage being there 87, the softening was no greater
+than at ground-level at pile A.
+
+It is probable that while the percentage of submersion in moving water
+hardly appears to affect the result, yet prolonged contact with wet
+sand, sea-weed, or clinging shell-fish may do so. This seems to suggest
+that the process of change, as between the sea-water and the iron, is
+slow, and to be effective must be continuous; so that it is only found
+to any considerable extent where the water in contact with the surface
+is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1
+foot and 6 inches above ground-level, the surface was in one pile
+shrouded in a thick mantle of heavy sea-weed, and in the other covered
+by molluscs; in both instances the surfaces being thus kept moist and
+undisturbed. The piles of the fourth case were in hard rock, were clean,
+and, where accessible, always either in moving water or quite dry.
+
+However this may be, the power to resist softening certainly appears to
+vary largely with the quality of the iron. The piles, referred to above,
+in which deterioration proceeded at the most rapid rate were certainly
+of a soft metal, the first being markedly so. On the other hand, certain
+piles (No. 4) of hard, close-grained iron suffered very little.
+
+It may be mentioned with respect to the last named, as a matter of
+interest, that the caps of the lower lengths (just above ground-level)
+had been cast with short pieces of wrought iron projecting--possibly for
+lifting purposes--which during thirty-eight years had altered in
+character to something very like softened cast iron, but laminated, and
+harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained
+having the semblance of wrought iron. The percentage of submersion was
+about 60.
+
+A number of piles, not included in the table, varying from fifteen to
+forty-four years old, and of the same structure to which set No. 2
+belonged, were all found to be hard, with the exception of one showing
+3/16 inch of softening. These are omitted, because the mud surrounding
+them was at the time of examination unusually high, so that the more
+normal ground-level could not be reached, at which points testing might
+have disclosed different results. It is probable that for any piles
+standing in soft material examination below the surface would reveal
+more pronounced softening than where occasionally exposed.
+
+To meet the effects of sea-water on cast-iron piles, and for other
+reasons, it is a common and good practice to make the lower lengths of
+greater thickness--say, 3/8 inch more--than that sufficient for the
+upper. Occasionally, also, the bottom lengths are filled with concrete,
+which no doubt adds to the length of time during which they may be
+relied upon.
+
+
+
+
+CHAPTER X.
+
+EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES.
+
+
+In the preceding chapters defects of various kinds to which riveted
+bridgework is liable have been more particularly dealt with; it is now
+proposed to consider the examination of such structures, following this
+by a reference to methods of repair and strengthening, leaving the
+treatment of other classes of bridgework to be developed under their
+proper headings, though some of the remarks immediately following will
+apply to all.
+
+The exhaustive survey of a bridge is only to be made after considerable
+experience in the work, but it may be stated that in looking for defects
+it is well to seek where they are least expected, till, with practice,
+one knows better where to direct attention. When examining with a view
+to pronouncing an opinion upon the fitness of the structure to remain in
+place, if in any real doubt, it is wise to give a casting vote against
+it; and finally it may be said that upon taking down a bridge condemned
+for any one or more defects, it should be examined for worse. This may
+seem to be somewhat pessimistic, but is based upon the teachings of
+experience.
+
+Preliminary examination of a bridge may reveal such faults or weaknesses
+as at once to ensure its condemnation; but if this is not the case, and
+there is a reasonable probability that the structure may be given a
+fresh lease of life, it will, for the purpose of estimating the
+strength, or for possible repairs, commonly be desirable to secure
+precise particulars of the existing structure independently of any
+drawings that may be in existence, and which will very probably be
+incorrect, the finished work, if old, seldom agreeing with the contract
+drawings. A final decision may in this case be deferred till after the
+measuring up has been completed, the condition of the structure becoming
+more familiar in the process.
+
+It is desirable first to ascertain whether the bridge remains in good
+form, whether the camber of girders appears to be what might be
+expected, or agreeable with existing records, though much reliance must
+not be placed upon figured cambers, it being quite common for girders to
+leave the bridge yards with the camber something other than that
+intended. The deflections under live load will also be observed, and
+compared with the calculated result, or checked by judgment. The
+calculations upon which strength and deflections are based will, of
+course, refer to the actual sections, which are sometimes a little
+difficult to ascertain if there has been irregular rusting. In
+continuous girders also, levels having been taken, allowance should be
+made for effects of settlement, if any; and with arches evidence of
+movement of the piers or abutments sought for, with the like object. It
+is seldom that the main flanges of girders show signs of weakness,
+unless from flexure in the case of long and narrow top members,
+insufficiently stiffened; but there may be want of truth from other
+causes already dealt with. In plate girders the webs should be most
+carefully scanned for possible cracks, particularly where cross-girders
+are connected, and along the upper edges of bottom flange angles, if the
+floor rest upon the flange. All riveted connections, of course, need
+close attention, both for straining effects, where there is a liability
+to wracking, and to detect loose rivets. Loose rivets and want of
+tightness in other parts of the work may frequently be detected at
+sight by a reddish bloom which appears on the neighbouring surfaces,
+caused by rust working out and spreading under the effects of weather;
+it may be seen round rivet-heads or along the edges of angle-bars, or
+other parts where there is movement. Loose rivets, though generally to
+be detected also by the hammer, may perhaps in the case of thin-webbed
+cross-girders be working in the web-thickness only, possibly to a
+considerable extent. This, if not otherwise evident, may sometimes be
+detected by simultaneous deflection tests--with rods--at the top and
+bottom flanges of a girder, at the same distance from the bearings. Any
+difference in the readings may indicate loose web-rivets, or possibly a
+tear in the web running parallel to the flange angles.
+
+Bracings between girders are very apt to display a rich harvest of
+working rivets. Cross-girders and longitudinals also may have loose
+rivets at their connections, and be very badly wasted, with quite
+possibly cracks in the webs, or other defects already enlarged upon.
+
+The condition of the road upon the bridge will frequently be an
+indication of the state of the floor which carries it; or the existence
+of rail-joints which are working badly may very properly lead to a
+critical examination of the girder-work immediately below, as this is a
+fruitful source of damage in light constructions. Floor-plates, where
+these exist, should be scanned for leakages, drainage nozzles, and
+guttering, to see that they are free, the attachments of the latter
+being often loose and unsatisfactory.
+
+Trough floors may be expected to show loose rivets near the ends, with a
+probability of excessive leakage where they abut against the webs of
+supporting girders.
+
+Floor plates resting upon abutments or piers, being very liable to
+serious decay, require attention, and girder-work entering masonry
+should receive close scrutiny, any obstruction to a sufficient
+examination being removed so far as is judged sufficient for the
+purpose. The structure should, of course, be closely watched during the
+passage of live load for any signs of abnormal movement, excessive
+vibration, or lurching.
+
+In addition to seeking for these various defects, or others which have
+been referred to in these pages at length, it will be well always to be
+alive to the possibility of faults to be seen for the first time, or of
+which the author has furnished no instance.
+
+Having formed a reliable opinion as to the state of the bridge, this, if
+satisfactory, may leave to be determined only the question of strength
+relative to the loads carried. It is apparent that stress limits
+suitable for a new structure, which has all its life before it, of
+purpose moderate to cover possible deteriorations, the growth of loads,
+and other adverse influences, may to avoid immediate reconstruction,
+reasonably be permitted of a higher value for a further term of years in
+the case of a structure which it is known has for a considerable period
+behaved well, and remains in good condition. What this higher value may
+be will be greatly influenced by the circumstances of each case, and,
+being largely a matter of judgment, may be expected to vary with
+different engineers. Experience shows, however, that the nominal unit
+stress in an old bridge may be a very considerable amount in excess of
+that allowed for new work, without, of necessity, showing any ill
+effects; and the author is of opinion that for old bridges in good
+condition it is quite prudent to allow an excess of 33 per cent. beyond
+that permissible for a new design. If the structure is too weak to
+satisfy this modified condition, it may be possible to bring it within
+the stress limit by a reduction of ballast or other removable dead
+weight. If this expedient does not promise to be satisfactory, or the
+bridge shows actual signs of weakness, or palpable defects, it will be
+necessary to deal with the question of repair, strengthening, or
+reconstruction.
+
+The repair of built up bridgework resolves itself largely into a matter
+of replacing loose rivets by cutting these out, rhymering the holes, if
+desirable, and again riveting. It will often be sufficient to do this
+with no particular precautions as to bolting up temporarily; the rivets
+having been loose, may very well be spared for a time. In re-riveting
+cross-girder connections it may, however, be imperative to remove all
+the rivets, bolting up securely as this is done, in order to make a
+tight job, taking out each bolt in turn as required, and again filling
+the holes; or it may be well in a bad case first to remove all loose
+rivets, substituting good bolts, in order that work which has gone out
+of shape owing to defective rivets may first be brought true.
+
+Cross-girder webs, cracked vertically or nearly so, are commonly
+repaired with splice-plates on either side; but in doing this it is
+undesirable to add plates of excessive thickness relative to the
+web--probably poor--as by an abrupt change of web section it appears not
+unlikely a fresh break may be favoured.
+
+[Illustration: FIG. 60.]
+
+[Illustration: FIG. 61.]
+
+[Illustration: FIG. 62.]
+
+[Illustration: FIG. 63.]
+
+Replacing wasted flange-plates, or adding new plates to those which
+exist, is occasionally resorted to in the case of main girders, the
+flanges of which are sufficiently accessible, but the operation is
+difficult, takes some little time, and should only be attempted under
+the constant supervision of a thoroughly capable man. When done, if the
+girder has not been relieved of load by staging, the stress under full
+load will be unequally distributed between the old and the new section,
+the old always taking more by the amount of the dead-load stress
+previously carried. The method which the author has seen applied to
+lattice girders of about 80 feet span, having good angle-bars in the
+flanges, with a shallow vertical web for attachment of diagonals,
+consisted in first cutting out the old flange rivets, and substituting
+bolts well screwed up, till all the rivets necessary had been removed.
+The new plate length having been prepared, was, on a Sunday, during a
+few hours' cessation of traffic, marked off, the temporary bolts being
+removed for the purpose, and then replaced. After the plate had been
+drilled, on a later Sunday, it was finally put into position, bolted up,
+and riveted at leisure; cover-plates make additional trouble, but are
+dealt with on the same principle. The method as shown in Fig. 60 is,
+however, barely practicable for so many plates. It is preferable, if it
+is proposed to add section, to do this with as little interference as
+possible with existing rivets of importance. This may be accomplished,
+if the existing plates are not too wasted at their edges, by riveting on
+new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength
+of a girder is increased by the addition to the top or bottom boom of
+material in such a form as sensibly to increase the depth, and thus,
+while adding increased section to one boom, to reduce the stress in
+each, though to dissimilar amounts. By this device also the relief is
+effective only as regards the live-load stress; under dead load only the
+new material does no work, provided, of course, that no relief staging
+was used during the alterations. For girders carrying any considerable
+proportion of dead load the method is very inefficient, though for
+others, in which the live load is relatively large, the result should be
+more satisfactory.
+
+As this question of adding new section to old is of much importance in
+dealing with repairs and strengthening operations, a few general remarks
+upon the subject will be pertinent. The difficulty in such work commonly
+is to cause the new to render any considerable assistance to the old in
+those cases which occur in practice. If a bar be imagined under
+longitudinal stress varying between 0 and a maximum, then, if the area
+of the piece be increased at the time when it takes no stress, its
+capacity for resisting the maximum amount will be increased, and for
+added material of similar elasticity the unit stress proportionately
+reduced. If, however, the load on the bar does not vary, the mere
+addition of metal will not relieve the original section in any degree.
+To take a third case, of the maximum being twice the minimum load, it
+will be necessary, in order to lower the maximum unit stress by 25 per
+cent., to double the original section of the bar if, as supposed, the
+extra metal has been added to the piece when under the smaller load, so
+that the new section is only effective in assisting to carry the
+remainder of the load at such times as it may be imposed. The
+relationship stands thus:--
+
+      Live load         New area
+  ---------------- x -------------- = relief.
+  Live + dead load   New + old area
+
+These statements will be true under the conditions named, within the
+elastic limit of the material; but some advantage would be derived in
+the second case, and a more marked benefit in the third, if the load
+assumed to be a maximum were exceeded, or if the composite bar were
+tested to destruction; as, however, these effects would be outside the
+limiting conditions imposed, it must be a matter of judgment as to how
+far this reserve of strength may be considered of value.
+
+If, instead of simply adding section to the bar, some part of the
+constant load is put upon the new section by the manner of attachment,
+the combination will, of course, be more effective.
+
+To apply these considerations and illustrate the way in which the two
+methods of adding flange section work out when reduced to figures, the
+case will be supposed of a girder 6 feet deep, carrying a load of which
+one-third is dead and two-thirds live. To the flanges of this girder are
+added plates equal to 50 per cent. of the original areas, in order to
+reduce the stress of 7 tons per square inch to which the girder before
+strengthening is liable, the depth remaining substantially unaltered.
+With dead load only the original section would be stressed to 2.3 tons
+per square inch, the new section being then unstressed. Under full load
+the new and old material take 3.1 tons per square inch additional,
+making the modified stress on the original section 5.4 tons per square
+inch, as against 7 tons; or a reduction of 22 per cent. This compares
+with 33 per cent., the relief due to 50 per cent. increase of flange
+area under ordinary conditions of stress distribution.
+
+Let the second method of strengthening the girder now be considered,
+using, for purposes of comparison, the same total amount of new material
+to increase the girder depth by an addition to the top flange. This
+section will be equal to the area of one flange, which, though it may
+be applied in many different ways, giving a greater or a less increase
+to the depth, would probably be used in some such manner as that shown
+in Fig. 64, increasing the effective depth for live-load stress by
+nearly 10 inches.
+
+[Illustration: FIG. 64.]
+
+The added material will, as in the previous case, leave the dead-load
+stress unaltered, or 2.3 tons per square inch. The stress in the bottom
+flange due to live load will, however, now be 4.1 tons per square inch,
+making a total stress of 6.4 tons per square inch, against 7 tons--the
+original stress. The reduction here is 8 per cent. only, as compared
+with 12 per cent., the relief due, under ordinary conditions, to an
+increase of effective depth from 6 feet to 6 feet 10 inches, and by the
+use of additional material, equal, as before, to one-half of the total
+flange areas before the alteration.
+
+The effect on the top flange need not be here gone into in detail, but
+it may be said that, owing to the increase of gross section and of
+depth, the ultimate stresses of both the new and old material are
+greatly less than as given for the bottom flange.
+
+Girders strengthened by the first of these two methods would, it is
+probable, if tested to destruction, give results more nearly in accord
+with the actual percentage increase of flange section, plastic
+deformation of the metal, before failure, tending to reduce the
+differences of stress on the new and old material of the sections.
+
+[Illustration: FIGS. 65 and 66.]
+
+Web members of lattice girders may, if weak, sometimes be dealt with by
+the introduction of supplementary bars, parallel to and between the old
+members, or by the addition of strips or angles to the existing
+diagonals. The treatment will be largely influenced by the nature of the
+old detail, which may lend itself to some one arrangement much better
+than to any other.
+
+End riveting of web members may, if it has become loose, be dealt with
+by simply rhymering the holes a size larger, and re-riveting in the best
+manner, if the stresses are not excessive; or it may be necessary to
+devise some additional attachments by which new rivets are brought into
+use (see Figs. 65 and 66). The effective relief due to supplementary
+rivets will be influenced by similar considerations to those governing
+increase of section.
+
+[Illustration: FIG. 67.]
+
+[Illustration: FIG. 68.]
+
+Old structures are very frequently deficient in bracing, which may, in
+such cases, be advantageously introduced; or girders individually weak
+may be rendered collectively efficient by suitable bracing. In
+considering the advisability of this, however, the case should be viewed
+with regard to the possible effects of such members, as already dealt
+with in the chapter relating to these questions. There it has been
+pointed out that bracing between a system of parallel girders may have
+the effect, under live load, of increasing the stress on the outer
+girders due to twisting of the structure as a whole, though the inner
+girders will, except for full loading of the whole bridge, be advantaged
+as to stress values, and in any event bettered by being held up to their
+work. The effect upon the outer girders may be met by increasing their
+strength, if this appears to be necessary. In all such alterations the
+detail should be schemed with special care to ensure simplicity in
+execution, smith's work being rigorously avoided. A good arrangement for
+supplementary bracing between plate-girders, which gives little trouble
+in carrying out, is shown in Fig. 67; or where the stiffeners of such
+girders are in line across the bridge, the detail given in Fig. 68 may
+involve less expenditure. Difficulties may be experienced in riveting,
+unless great care is taken in the positioning of rivets. Fitting-bolts
+are only to be relied upon as such, if they really justify the name;
+they are, though easy to specify, by no means easy to secure under the
+conditions of practical work. Weak cross-girders may make
+alterations--in some cases considerable--necessary, to rectify the
+defect of strength. The removal of old girders to make room for new is
+seldom resorted to, unless the existing detail renders this a simple
+operation; but it is not unusual to introduce new girders between the
+old in cases where there is no plated floor to make the work difficult.
+By this method there is, of course, an increase of appreciable amount in
+the dead load carried by the main girders, which would in many instances
+be objectionable. With deep and heavy main girders, having plate webs,
+cross-girders may be strengthened by improving the end connections by
+suitable gussets, and attachment to good vertical stiffeners, the fixity
+of the ends thus aimed at being assured by overhead struts or girders,
+from one main girder to its fellow, at intervals apart well considered
+with reference to the horizontal strength of the top flanges, the whole
+thus making a closed frame, as shown in Fig. 69. The method appears
+feasible, but it should be stated that the author has not known it to be
+applied in its entirety as a means of strengthening an old floor.
+
+[Illustration: FIG. 69.]
+
+A simple and very common device consists in substituting for the
+ordinary cross-sleeper road, where this exists, stout timber
+longitudinals under the rails, which have, where the cross-girders do
+not exceed 5 feet centres, a marked distributive effect, tending to
+reduce the maximum load upon any individual girder. With a similar
+object, trough girders containing longitudinal timbers are sometimes
+adopted where the depth available is not enough to enable sufficiently
+stiff timbers to be used alone. In either case the object sought is the
+same--to modify the effect of the heavier wheel loads upon isolated
+cross-girders. When the spacing is so close as 4 feet, the beneficial
+result of this treatment is considerable, but at 8 feet centres it can
+have but a moderate effect where timbers alone are used.
+
+Occasionally, for long cross-girders, a distributing girder is placed,
+with the same intent, in the 6 feet way, its function being limited to
+this use only if the depth and strength are sufficiently small to serve
+this object alone, as distinct from the case in which it becomes a
+carrying girder transferring load to the abutments. As a distributor
+simply, the girder has to equalise the bending moments amongst the
+cross-girders, to effect which it will be evident that these moments
+having been ascertained for the several cross-girders previous to
+alteration, for a position of the wheel loads such that the heaviest
+comes upon a centre cross-girder, the mean of these moments will, when
+compared with that for each girder, show the difference to be induced as
+a result of introducing the distributor. These differences of moment
+render necessary at the centre of the cross-girders reactions upwards or
+downwards, as the case may be, of amounts competent to induce moments
+below the inner rails equal to these differences.
+
+It is these reactions which must be provided by the distributing girder
+at a moderate stress, and without flexure of such an amount as sensibly
+to modify the reactions. The greatest section necessary at any one point
+may then be adopted for the girder throughout. The result will commonly
+work out to a moderate section, but there will be no harm in a little
+excess in a case of this kind, the total cost being but little affected
+by some small addition to the weight, where labour upon the site is so
+considerable an item as in work of this description. The ends of the
+distributing girder should be carried on to the abutments or piers to
+ensure adequate relief of the end cross-girders. It will be found
+desirable in arranging for distributing girders to ascertain at an early
+stage, by boning or by levelling, the condition of the cross-girders as
+to uniformity of heights, as this may affect the length most suitable
+for separate sections. Between the underside of the distributor and the
+cross-girder tops there will commonly be spaces of varying amounts,
+which should be filled by packings to fit, rather than by pulling the
+work together by force, introducing undesirable stresses of uncertain
+amount.
+
+In the earlier remarks upon the strengthening of bridgework by the use
+of new material, it has been assumed that the modulus of elasticity of
+the new metal is similar to that of the old; it may, however, as in
+cases where wrought-iron work is reinforced by additions in steel, be
+necessary to take the difference of elastic properties into account,
+with which object the new section should be multiplied by a quantity
+(greater or less than unity) inversely proportional to the higher or
+lower modulus of the new material, that is to say, by
+
+  E of old material
+  -----------------
+  E of new material
+
+
+
+
+CHAPTER XI.
+
+STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS.
+
+
+The addition of distributing girders, described in the last chapter, as
+a means of strengthening a bridge floor, while sufficient in many cases
+so far as the cross-girders are concerned, does not in any appreciable
+way assist the main girders. When for a two-line bridge, having outer
+main girders only, this result also is desired, together with a more
+complete relief of the floor structure, centre main girders may be used,
+placed either above or below the cross-girders, on the centre line of
+the bridge.
+
+There are two principal ways in which such a girder may be brought into
+use; the easier, but generally less economical, is by making a simple
+attachment to the cross-girders, the old girder work still taking the
+whole dead load. By this method the new girder does no work but carry
+itself till the live load comes upon the bridge, and must be made very
+stiff to take any sensible portion of the running load; the second
+method is to make the connection adjustable, so that a part of the floor
+weights may be imposed upon the new girder as an initial load. In doing
+this the old outer girders will rise slightly, being relieved of stress,
+and the cross-girders also lifted at the middle, whilst the new girder
+is depressed as the load is brought upon it. With some part of the live
+load a very considerable proportion of the total may in this way be
+carried by a centre girder of moderate section. The whole question, by
+either method, turns upon deflections; and it is in determining the
+relative movements of the girders that the problem chiefly lies.
+
+It is convenient first to determine the percentage of load relief to be
+effected in the main girders, as to which it is to be observed that as
+this relief (distributed) is induced by the upward reaction of the new
+girder acting at the centre of the cross-girders, the stress relief of
+these will, as a rule, greatly exceed that of the outside girders. For
+the generality of cases, it may be taken that the relief suitable for
+the outside girders will be satisfactory in its effects upon the
+cross-girders, even though it is desired to reduce the stress in these
+to a greater degree.
+
+If, however, it be thought desirable to check this, it may be done by
+considering a cross-girder subject to its dead and live loads acting
+downwards, and to reactions at the centre and ends. At the centre the
+reaction will be the load of which the two main girders are relieved on
+a length equal to the pitch of the cross-girders, or as here given:--
+
+  _c_ x _t_ x P = reaction at centre (1)
+
+_c_ being the percentage of relief; _t_ the total load per foot run of
+the bridge; and P the pitch of cross-girders. The live loads carried by
+the cross-girders are for this purpose taken at per foot run, as for the
+main girders. With these data it will be easy to construct a diagram of
+moments, making it evident whether the relief proposed for the main
+girders will give a sufficient percentage of relief to the floor beams.
+
+Granting that this proportion has been decided, and dealing first with
+the case in which the centre girder is simply attached to the
+cross-girders, and takes no dead load other than its own weight, then
+the live load carried by the outside girders, and previously borne
+wholly by them, will be reduced by the amount it is intended to transfer
+to the centre girder, and will become
+
+  L{_l_} - (_c_ x L{_t_}) = live load on outer girders (2)
+
+L{_l_} being the total live load, and L{_t_} the total dead and live
+load carried by the bridge. From this the deflection of the outer
+girders corresponding to this modified live load may be derived.
+
+[Illustration: FIG. 70.]
+
+It is next necessary to ascertain the vertical movement, commonly a
+depression, of the cross-girders at the centre relative to their ends,
+when subject to the running load only, and supported at the middle and
+ends, the centre reaction being obtained as before indicated (1). This
+movement will be the difference (if any) between the deflection on the
+whole span of the cross-girder due to the live load, and the upward
+flexure of the girder due to the centre reaction, considered as separate
+effects. Stress values having been estimated for the two conditions,
+these results may readily be deduced by simple flexure formulae,
+observing that while the curve of moments due to live load sufficiently
+approximates to that for a distributed load to justify, for this, the
+use of a distributed load formula as given in the chapter "Deflections,"
+the flexure due to the centre reaction will be but 0.80 of that which
+corresponds to the same stress for distributed loading. Or, the curve
+assumed by the girder under live load may be plotted by a method to be
+later explained.
+
+The sum of the movements now determined--that is, the live-load
+deflection of the outer girders, and depression, as is commonly the
+case, of the cross-girders--will give the extreme depression (marked _m_
+in Fig. 70), from the dead-load condition of the middle cross-girders,
+when supported to the extent desired by a centre girder whose
+proportions are not yet known, but which, carrying the required
+percentage of the total load, must, subject to a reservation presently
+stated, deflect only this amount. The unit stress in the flanges of the
+new girder, governed by this flexure, will for a plate girder be
+
+  D x C x _m_
+  ----------- = _f_, unit stress on gross section (3)
+       S squared
+
+D and S being, as before (see "Deflections"), the depth and span
+respectively in feet, C a constant, _m_ the deflection in inches, and
+_f_ the stress per square inch on the gross section of flange.
+
+The gross area A, of the flange, is given by
+
+  S x _c_ x L{_t_}
+  ---------------- = gross area of flange (4)
+    8 x D x _f_
+
+_c_ x L{_t_}, being, as in (2), the load transferred to and carried by
+the centre girder.
+
+The actual stress in the flanges will, of course, be greater by an
+amount due to the girder's own weight; but this does not affect the
+question of relief. For any ordinary case the stress per square inch
+will be low; but it will manifestly be useless to assume a greater
+stress with a view to economy, as the effect of reducing the section
+will simply be to make the girder too flexible, thus causing it to be
+less effective than primarily intended. If, as is seldom the case, there
+is freedom as to the depth of girder permissible, it is evident the unit
+stress may be made a condition, and the depth deduced by a suitable
+modification of formula (3); the relief desired being in this way
+equally well assured. Indeed, in the rare instances in which any depth
+may be adopted, this method is--contrary to the general rule--distinctly
+economical, particularly if the girder may be placed below the
+cross-girders, which simply rest upon it, without elaborate attachments.
+
+[Illustration: FIG. 71.]
+
+Considering now the second method of applying centre girders by which
+the new girder is made initially to carry part of the dead load, by
+adjustment, it will at once be recognised as a more complex matter. The
+measure of relief by which the old girderwork shall benefit need not be
+affected by the method of applying the centre girder, and may be decided
+on the principles already considered. The outer girders carrying a
+reduced load, when the bridge is fully loaded, and the cross-girders
+being in part supported at their centres in the manner already
+described, will give a resulting depression _m_ (see Fig. 71) of the
+centre cross-girders, below the original dead-load position, of a
+similar amount determined in the same way. This extreme depression
+determines also the lowest position of the new centre girder, which may
+be designed to carry the required percentage of the total bridge loads
+with the maximum stress and depth, as conditions, leaving the initial
+dead load and necessary adjustments to be ascertained. This is the
+common case and will be here dealt with, it being assumed to avoid
+ambiguity in description that the new girder lies above the
+cross-girders.
+
+The centre girder of fixed depth being then required to carry a definite
+load at a definite flange stress, will deflect a definite amount at this
+stress. If this deflection equalled the extreme depression _m_ of the
+old girder work, no adjustment would be necessary, the centre girder
+then carrying no initial dead load, as by the first method; but for
+centre girders designed for economical flange stress the deflection will
+in ordinary cases greatly exceed this, the depth generally being small,
+and in order to ensure that the new girder shall do its full work, some
+dead load must be put upon it. In the act of adjustment the
+cross-girders must be lifted and the centre girder depressed, till the
+joint movement equals the excess _s_ of the centre girder deflection
+over _m_, when the new girder will carry the proper amount of initial
+load, and upon further deflection under live load give the full measure
+of relief. The amount of "lift" or upward flexure of the old girder
+work, and the depression or "drop" of the new girder, during adjustment,
+will depend upon relative stiffness, and may be ascertained as
+follows:--
+
+For unit reactions at the centre of the cross-girders the upward flexure
+of these may be ascertained, as also the upward flexure of the two outer
+girders when subject to forces of the same total amount (one-half to
+each) applied at the cross-girder ends. The sum of these movements will
+give the total lift of the centre cross-girders, when all are subject to
+unit lifting forces; similarly, the depression of the centre girder for
+unit loads applied at the cross-girders may be determined. There will
+then be known the movements upwards and downwards of the old and new
+work when being drawn together by unit forces applied as stated.
+
+If
+
+  _l_    = lift due to unit loads,
+  _l{t}_ = total lift due to adjustment,
+  _d_    = drop due to unit loads,
+  _d{t}_ = total drop due to adjustment,
+  _s_    = deflection excess = gross adjustment,
+
+there will then be
+
+     _d_
+  --------- x _s_ = _d{t}_,
+  _l_ + _d_
+
+total drop of centre girder under adjustment,
+
+     _l_
+  --------- x _s_ = _l{t}_,
+  _l_ + _d_
+
+total lift of centre cross girders under adjustment,
+
+  _d{t}_
+  ------ x unit load =
+   _d_
+
+initial load put upon centre girder at each cross-girder.
+
+The rise of the two outer girders for upward forces together equal to
+those depressing the centre girder may readily be deduced.
+
+[Illustration: FIG. 72.]
+
+[Illustration: FIG. 73.]
+
+The act of adjustment may conveniently be effected by the arrangement
+shown in Fig. 72, in which each cross-girder is hung up at its centre by
+four bolts. At the middle of the centre girder the total amount to be
+screwed up will be that corresponding to the deflection excess _s_, but
+towards the ends this amount decreases, and may advantageously be
+represented by a diagram as Fig. 73, in which, if _s_ represents to
+scale the amount to be screwed up at a centre cross-girder, the
+corresponding amounts for other girders may be read off direct. It will
+be apparent that it must be necessary to place the centre girder at
+such a height as to leave a space between the old and the new work
+greater than the amount to be screwed up, this excess clearance being
+ultimately filled by a packing.
+
+The precautions to be observed in carrying out this kind of work, and
+the practical methods of adjustment adopted by the author after some
+little experience, may here be given.
+
+Great care is necessary at the outset to ascertain the true spacing of
+the cross-girders, to ensure that the bolt-holes in the bottom flange of
+the centre girder shall come where desired. The fixing of the
+cross-girder brackets also needs close attention to avoid after trouble,
+the bolt-holes in the brackets being preferably drilled on the site
+after fixing. It will, for masonry abutments, be necessary to fix
+bedstones to receive the new centre girder, which, being carried out
+quite possibly under adverse traffic conditions, will perhaps leave the
+stones liable to settle slightly when the full load is carried. To
+eliminate the bad effect of this upon the ultimate adjustment, and to
+take up any initial set of the new girder work, which would be
+prejudicial in the same way, it is desirable, the centre girder being in
+place, to screw up the bolts temporarily and leave the work for a week
+or two. To ensure regularity in the screwing up process, it is
+convenient to prepare, for use at the bridge, a diagram somewhat similar
+to Fig. 73, giving the amount by which the new and old work are to be
+brought together at each cross-girder, with the number of turns for each
+nut to effect this. With a man at each side of the girder, the whole
+length is traversed, giving a half-turn to each nut; this is repeated as
+often as necessary, and so managed as to bring all up proportionately to
+the final requirement, keeping tally with chalk marks over each
+cross-girder as a check. The preliminary screwing up should be conducted
+with little less care than that adopted for the later adjustment, to
+avoid damage to the old work. This later adjustment having in due course
+been effected, it is then necessary to measure for packings to fill the
+spaces remaining between the old cross-girders and the new centre
+girder. These spaces should be callipered at each of the four corners,
+care being taken to avoid after-confusion. The measurements ascertained
+will, however, be too great for the finished packings, as an allowance
+of not less than 1/10 inch (total), will commonly be wanted to cover
+irregularities in the surfaces. The packings, having been prepared and
+checked, may be slipped into place after slacking all the bolts a small
+amount to permit this to be done, finally screwing up tight and securing
+the nuts by split-pins, through holes drilled as the last operation.
+
+As a check upon the calculations and adjustment, the "lift" of the outer
+girders and cross-girders, and the "drop" of the centre girder may be
+observed by levelling. For this purpose the author has used a staff of
+inches divided into tenths, with which, and a good level, very accurate
+readings may be taken for short distances.
+
+No reference has been made to the effect of skew in a bridge on the
+above methods, the explanation given applying rather to bridges square
+on plan. The influence of skew on the load distribution will largely be
+a matter of detailed calculation. The flexure of the girders may also be
+sensibly affected, but may be arrived at with sufficient accuracy
+without any great trouble. The chief effect of skew is to modify the
+amount of screwing up during adjustment, which may be better understood
+by reference to Fig. 74, and comparing it with Fig. 73, the adjustment
+diagram for a square bridge.
+
+To illustrate how these methods of strengthening work out, and compare
+as to weights of centre girders required, the case has been assumed of a
+wrought iron bridge of 60-feet span, having outer girders 5 feet deep,
+of 39 square inches gross flange area; and cross-girders, at 8-feet
+centres, 27-feet span, 1 foot 9 inches deep, with a gross flange area of
+twenty square inches. The dead load and live load on either road are
+each 1.75 tons per foot run.
+
+The stress in the outer girders previous to the alteration being 6 tons
+per square inch gross, it is desired to relieve this to the extent of 33
+per cent. by a steel centre girder. In the table here given the
+quantities given in italics are fixed as primary conditions:--
+
+CENTRE STRENGTHENING GIRDERS FOR 60-FT. SPAN.
+
+  ----------------------------+-----------+------------+------------
+                              |  Centre   |  Centre    |
+                              |  Girder,  |  Girder,   |Adjustments
+              --              |  Stress   |   Depth    | Unknown.
+                              |  Unknown. |  Unknown.  |
+  ----------------------------+-----------+------------+------------
+       _Outer Girder._        |           |            |
+                              |           |            |
+  Deflection under modified   |           |            |
+  live load                   |  .42 in.  |  .42 in.   | .42  in.
+  Lift of adjustment          |   _nil_   |   _nil_    | .153  "
+                              |           |            |
+      _Cross Girders._        |           |            |
+                              |           |            |
+  Depression under live load  |           |            |
+  --modified conditions of    |           |            |
+  support                     |  .13 in.  |  .13 in.   | .13   "
+  Extreme depression (_m_)    |  .55  "   |  .55  "    | .55   "
+  Lift of adjustment (cross-  |           |            |
+  girder only)                |   _nil_   |   _nil_    | .095  "
+  Total lift of adjustment    |           |            |
+  (_l{t}_)                    |   _nil_   |   _nil_    | .248  "
+                              |           |            |
+      _Centre Girder._        |           |            |
+                              |           |            |
+  Depth                       | _3.5 ft._ |  8.2 ft.   |_3.5 ft._
+  Unit stress on gross section|           |            |
+  (ex girder's weight)        | 2.14 tons | _5.0 tons_ |_5.0 tons_
+  Total deflection (ex        |           |            |
+  girder's weight)            |  .55 in.  |  .55 in.   |1.28 in.
+  Deflection excess (_s_)     |   _nil_   |   _nil_    | .73  "
+  Depression, or "drop" of    |           |            |
+  adjustment (_d{t}_)         |   _nil_   |   _nil_    | .482 "
+  Gross area of flange        |105 sq. in.|19.2 sq. in.|44.5 sq. in.
+  Weight                      |  20 tons  |  10.4 tons |11.4 tons
+  Net flange stress (including|           |            |
+  girder's weight)            | 3.19 tons |  6.87 tons | 6.94 tons
+  ----------------------------+-----------+------------+------------
+
+Girders subject to distributed load are treated as having uniform
+stress, but where this is not strictly the case, as in some light
+girders, it will be necessary to take the fact into account. For centre
+girders of wrought iron, and a unit stress on the gross section of 4
+instead of 5 tons, the girder weights are between 9 and 10 per cent.
+greater.
+
+[Illustration: FIG. 74.]
+
+In the above treatment of the application of centre strengthening
+girders there is a source of error which should be touched upon. If,
+under live load, the centre girder deflects more than the outer girders,
+as it commonly will, there must be a want of uniformity in the behaviour
+of the cross-girders, those near the abutments being more relieved than
+the estimated amount of relief of those at the centre, which will have
+less than that intended; but the reduction of stress in the
+cross-girders will generally be so considerable that any such ambiguity
+of excess or defect is commonly unimportant; the effect of this also
+upon the main girders is much less than might be supposed, being, for
+the third of the cases just given, about 2-1/2 per cent. excess for the
+centre girder, and generally a much smaller error. With this
+qualification, the method can, however, be regarded as approximate only.
+It is possible to eliminate some part of the error by lifting the end
+cross-girders during adjustment, a less amount than that given by the
+diagrams, Figs. 73 and 74, taking care that the centre girder is
+depressed its full amount by lifting the centre cross-girders a little
+more; this refinement is hardly necessary, and unless controlled by
+calculation cannot be depended upon for precise results.
+
+Particulars are here given of five ordinary cases, comparing the
+calculated and observed results of adjustment. The operation of
+levelling was conducted by a quick-eyed and capable assistant, who was
+not made acquainted with the results expected, in order to avoid any
+sub-conscious tendency to match the calculated figures:--
+
+EXAMPLES OF CENTRE GIRDER ADJUSTMENTS.
+
+  ---------------------------------------+-----------+-----------------
+                    --                   |Calculated.|    Observed.
+  ---------------------------------------+-----------+-----------------
+                                         |   in.     |    in.
+                                         |           |
+                          No. 1.--56-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   .82     |    .84
+  Lift of cross-girders at centre        |   .23     |    .22
+  Lift of outer girders                  |   .20     |.10 and .13
+                                         |           |
+                          No. 2.--57-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   .50     |    .50
+  Lift of cross-girders at centre        |   .18     |    .20
+  Lift of outer girders                  |   .11     |.08 and .10
+                                         |           |
+                          No. 3.--67-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   .70     |    .75
+  Lift of cross-girders at centre        |   .15     |    .17
+  Lift of outer girders                  |   .10     |    .09
+                                         |           |
+                          No. 4.--68-_Ft. Span._
+                                         |           |
+  Depression of centre girder            |   .70     |    .65
+  Lift of cross-girders at centre        |   .20     |    .18
+  Lift of outer girders                  |   .13     |    .14
+                                         |           |
+            No. 5.--52-_Ft. and_ 28-_Ft. Spans continuous._
+                                         |           |
+                                         |Long |Short|Long |Short
+                                         |Span.|Span.|Span.|Span.
+  ---------------------------------------+-----+-----+-----+-----------
+                                         | in. | in. | in. | in.
+  Depression of centre girder            | .28 | ..  | .29 | ..
+  Lift of centre girder                  | ..  | .04 | ..  | .03
+  Lift of cross-girders (centre of spans)| .17 | .09 | .15 | .13
+  Lift of outer girders                  | .08 | ..  | .08 | ..
+  Depression of outer girder             | ..  | .01 | ..  |negligible.
+  ---------------------------------------+-----+-----+-----+-----------
+
+The method of calculation adopted for these cases was not precisely that
+given, though depending upon the same broad principles. The first cannot
+be considered a good example. The last, having continuous girders, of
+course needed special treatment.
+
+Of about seventeen bridges strengthened in the manner described, the
+effect generally was satisfactory, in reducing deflection and vibration;
+but in two cases of small span, owing probably to settlement of
+bedstones, the results were not so good.
+
+From first to last the work of putting in a centre girder takes some
+little time, owing to the slow progress generally made in fixing the
+brackets, preparing packings, etc. The cost of a typical case was about
+23 per cent. of the cost of a new superstructure, with a 30 per cent.
+relief of stress.
+
+[Illustration: FIG. 75.]
+
+[Illustration: FIG. 76.]
+
+A special case of strengthening by a centre girder, having considerable
+interest, may be here referred to. The primary idea involved was not the
+author's. The bridge dealt with has already been noticed under "Bracing"
+and a section, before alteration, shown in Fig. 26. The span being 85
+feet, there was no room for a centre girder of sufficient depth above
+the cross-girders and between the roads, nor was it considered
+economical to place the girder wholly below the floor, because of the
+costly staging this would have necessitated for erection purposes, the
+height above ground level being very great. A girder was therefore
+designed, having open latticing at an angle of 60 degrees, with a bottom
+boom to be below the cross-girders, the top being as high above the
+rails as could be permitted (see Figs. 75 and 76). A temporary boom was
+arranged at the intersection of diagonals, the lower boom proper not
+being fixed till the girder having been lifted into place, with the
+diagonal members passing between the cross-girders, allowed this to be
+done. The girder for some time carried itself from bearing to bearing,
+with the temporary boom in tension, the deflection being then 2 inches.
+The permanent boom was then put in place, and the girder restored as
+nearly as was practicable to the camber it was intended to have when
+complete, but without throwing, during the process, any improper loads
+upon the old work.
+
+The lower boom being finally riveted up, the cross-girders were made to
+bear upon it by suitable packings. There were, in addition to the new
+girder, two stiff frames between the old main girders, to which the new
+was secured.
+
+The girder was designed with the intention that under dead load only the
+cross-girders should just rest, but throw no weight, upon the new work,
+the latter assisting to carry live load only. The floor beams being of
+small span, and securely riveted to the old girder tops, the centre
+girder was required to deflect, under its share of live load, the same
+amount as the old main girders under the remaining portion, the three
+points of support of the cross-girders thus not altering their relative
+levels. That this resulted was evident from the fact that, previous to
+connecting the cross-frames to the centre-girder, the work being
+otherwise complete, a space between the two of about 1/2 inch,
+afterwards filled by a packing, showed no alteration, the closest
+measurement failing to disclose any relative movement upon the passage
+of live load. The reduction of vibration was, as might be expected, very
+marked.
+
+In the conduct of that class of strengthening work which has been dealt
+with in this chapter, it is essential, in the author's judgment, that
+the man responsible for the detailed calculations and design should
+himself see the operations of adjustment carried out, or delegate it
+only to one equally familiar with the requirements.
+
+Before dismissing the subject, it will be well to refer to a method of
+approximately determining flexure curves, of occasional use in dealing
+with centre girder or similar questions. The figure assumed is plotted
+to an exaggerated scale, with which object the actual radius of
+curvature at points along the girder's length are first ascertained by
+the formula
+
+   E x D
+  ------- = R, radius of curvature in feet,
+  _f_ x 2
+
+and the radius of curvature for the diagram by
+
+  12 x R x F squared = _r_, radius for plotting, in inches (5)
+
+E being the modulus of elasticity, D the girder's depth in feet, _f_ the
+mean of the extreme flange stresses per square inch of gross area, and F
+the fraction indicating scale as 1/48, where 1/4 inch = 1 foot. The
+curve, being plotted, shows by direct scaling the movement of any point
+relative to its original position. Near the ends of the curve where the
+radii may be of considerable length, the arcs may be drawn with the help
+of template curves, or even set out as pieces of "straight."
+
+When the curve is laid down so that its chord equals the span to scale,
+the method involves an error of excess in the resulting deflection or
+droop which is as much as 7 per cent. when the mean radius for plotting
+equals the span as drawn, or when the droop of curve approaches
+one-eighth of the span. As the exaggeration of curvature is made less
+pronounced, this error rapidly diminishes, till for a droop of about
+one-sixteenth the percentage is one-fourth part of that above given.
+This excess in the droop of curve may be amended by the following
+expression:--
+
+          (droop cubed       )
+  droop - (------ x 3.73) = corrected droop, or deflection.
+          (chord squared       )
+
+For some purposes it may be preferable to amend the radii for plotting,
+so that the curve, as laid down, shall be correct, which may be
+effected by the formula here given, to be applied to each value of r, as
+first ascertained:--
+
+        (chord squared        )
+  _r_ + (------ x .0625) = corrected plotting radius.
+        (  _r_         )
+
+If, however, the length of curve is made equal to the span (the chord
+then being less), and the radii for plotting as given by (5) are used,
+the result will for most purposes be sufficiently precise, though there
+will now be an error of a contrary kind, which, for a curve having a
+droop of one-eighth, will be about 2 per cent. too little. A somewhat
+similar method of setting out deflection curves is described by
+Professor Fleeming Jenkin in the article "Bridges" of the "Encyclopaedia
+Britannica," but without corrections.
+
+A careful comparison of results by the above means, with those
+calculated, shows that with good draughtsmanship they may be relied upon
+for considerable accuracy. Equally applicable to girders of varying
+depth and flange stress, they have also a limited use in cases of
+continuity.
+
+[Illustration: FIGS. 77 and 78.]
+
+Figs. 77 and 78 illustrate the deflection and stress diagrams for the
+cross-girders of the bridge supposed to have been strengthened by a
+centre-girder, when under the influence of live load and a centre
+reaction of a definite amount. As a matter of convenience, each radius
+length has been halved, before correction, so that the resulting droop
+of the curve is twice the true amount.
+
+
+
+
+CHAPTER XII.
+
+CAST-IRON BRIDGES.
+
+
+Cast Iron as a material for bridges has of late years fallen into
+disrepute. It is now entirely tabooed by the Board of Trade for railway
+under-bridges, unless of arched construction. This condemnation of cast
+iron followed, and was apparently the result of, an accident which
+occurred to an under-bridge on one of the southern lines, which bridge
+had already earned for itself an ill repute by breaking down on a
+previous occasion. The ultimate issue was, however, good, inasmuch as it
+led to a thorough overhaul of all railway under-bridges in this country,
+and the renewal of a great number no longer in a condition suited to the
+carriage of heavy or of passenger traffic; yet there is little doubt
+that, in the author's judgment, many excellent cast-iron bridges were
+then removed at considerable cost, to be replaced by others of wrought
+iron or steel, which will not last so long as many of those displaced
+had done, or would still have lasted had they not been dismantled.
+
+The earlier cast-iron bridges were commonly made of cold-blast iron, a
+material of such strength and toughness as to give an extraordinary
+amount of trouble in breaking up the heavier parts, when the time
+arrived to do this, and with which material ordinary hot-blast iron is
+not to be compared for reliability.
+
+[Illustration: FIG. 79.]
+
+As illustrating the very considerable stress to which cast iron may be
+subjected, without of necessity leading to any mishap, two cases may be
+cited. The first, a bridge of 32 feet effective span, carrying two
+lines of way, each pair of rails being supported upon Barlow rails,
+forming the bridge floor, the ends resting upon the bottom flanges of
+inverted [T]-shaped girders, 2 feet 3 inches deep, as shown in Fig. 79.
+
+The extreme fibre stress works out at 2.9 tons per square inch in
+tension, and 5.9 tons per square inch compression, calculated as it
+would be in ordinary office work; but for the actual loads, at a span as
+above, exceeding the clear span by 6 inches only, and without regard to
+the effects of eccentric application of the load. The girders when taken
+out showed upon examination no sign of overstrain. The practice of
+loading cast-iron girders in this manner cannot, however, be too
+strongly condemned, notwithstanding that in this case no ill resulted.
+It is evident that a piece of the lower flange being broken out from
+this cause, as occasionally happens, might so reduce the section as to
+result in complete failure.
+
+[Illustration: FIGS. 80 and 81.]
+
+The second example is that of a small railway under-bridge of two spans,
+continuous over the central pier, each span being 16 feet 6 inches. The
+rails were supported upon longitudinal timbers lying within
+trough-shaped girders, as shown in Figs 80 and 81.
+
+The stress over the pier, in the extreme fibres of the top flange, is
+estimated at 4.7 tons per square inch in tension, but it should be noted
+that the effect of the timber longitudinal and rail has been neglected
+in arriving at this result, which might possibly on this account be
+reduced to near 3 tons per square inch.
+
+The case is noticeable because no evidence of high stress was apparent.
+The author saw nothing to suggest sinking of the central pier, the
+effect of which, within limits, would be to further reduce the stress as
+calculated; but it is quite possible some slight settlement had
+occurred; this, as the spans were so small, would have a sensible
+effect. While too much reliance should not, it is clear, be placed upon
+any estimated result about which there is a lingering doubt, it should
+be remarked that, as it would be necessary the pier should sink 3/16 of
+an inch, for each ton of reduced stress, it is not probable that the
+results quoted are in excess to any material degree; they are, indeed,
+more probably low, as no notice has been taken of impact.
+
+Though cast-iron girders for railway under-bridges are now prohibited in
+this country for new works, there are still uses to which they may be
+applied, and it may be well to insist that girders of this material
+should be fairly loaded, the weight being brought upon them in such a
+way that there shall be no serious secondary stress, such as arises when
+wide flanges are made to carry concentrated loads; the author has,
+indeed, met with no instance of a cast-iron girder breaking down under a
+load fairly applied. Preference is now given to steel or wrought iron
+for columns; while this is often quite justifiable, there remain many
+cases in which nothing better need be desired for this purpose than good
+cast iron, provided only that the column be loaded in a suitable
+manner--i.e., axially, and that the arrangement and details of the
+super-structure are such that there shall be no cross-breaking efforts,
+or rocking of the column due to temperature or other causes; unless,
+indeed, such cross-breaking or rocking is definitely taken into account
+in designing the work. The same care observed in the detailing of
+cast-iron work that is not infrequently taken in the design of
+structures made of rolled sections would, in suitable cases, the author
+has no doubt, yield results just as reliable in practice, with the
+advantage of greater resistance to rust, and a reduced cost in
+maintenance.
+
+Good cast iron is, in fact, when used with discretion, a most excellent
+material, popular predjudice notwithstanding. The oldest metallic bridge
+in this country at the present moment is of that metal.
+
+The one chief respect in which cast iron is at a disadvantage compared
+with wrought iron or steel is that it does not give premonitory warning
+of failure--it remains intact, or it breaks. The indications of
+weakness, which may be read by an experienced inspector of other
+metallic bridges, are in a great measure absent. There is also an
+objection which may exist, but is to be avoided by good design and care
+in the foundry--viz., internal stress due to unequal cooling. In extreme
+cases this may lead to fracture before the work has left the maker's
+hands, but it can only occur by neglect of ordinary precautions.
+
+[Illustration: FIGS. 82 and 83.]
+
+In a case which has already been referred to in the chapter on
+"Deformations," page 80, an outer rib of a cast-iron arch fractured near
+the crown after fifty-four years' use. Owing to the nature of the
+design, and the fact that the near abutment had closed in slightly,
+bringing the linear arch of necessity near the lower edges of the arch
+segment in question, it was possible to estimate, with a probability of
+truth, the extreme fibre stress (tensile) due to the load forces, at the
+upper edge where fracture commenced. The result was very far from
+explaining the occurrence of the break, but an examination of the
+details shown in Figs. 82 and 83 will make it apparent that, in addition
+to the tensile stress, as calculated, there was probably a severe
+initial stress of the same character due to irregular cooling in the
+foundry half a century before. The sum of these stresses, it is
+suggested, placed this particular casting in a critical condition, such
+that operations in the construction of a new bridge adjacent either by
+producing a small further settlement of the foundations, of which the
+author saw no evidence, or, as is more probable, the attachment of a
+rope to this rib for the purpose of keeping a barge in position, which
+certainly did occur, gave the arch rib just such an additional strain as
+to result in the break shown, though no one of these causes acting
+singly would have been sufficient to induce fracture. The inner ribs
+were of a much less objectionable section.
+
+[Illustration: FIG. 84.]
+
+Cast-iron arches, though still allowed by the Board of Trade rules, are,
+indeed, liable to be seriously affected by settlement, or yielding of
+the abutments, unless hinges at the crown are introduced. As an instance
+of this may be quoted a bridge of some 45 feet span, in which the arches
+were cast in two pieces abutting, and very efficiently bolted together
+at the crown, the springing and vertical abutment member of the
+spandrel being bolted and built solidly into heavy masonry. The arch
+sank at the crown, caused by, or itself the cause of, a movement of the
+abutment, with the result that the lower bolts at the crown joint broke
+away, rupturing the casting, as shown in Fig. 84. The arch must then
+have acted as though hinged at the crown, as effectiveness of the
+connection was destroyed. It had been better, evidently, if a proper
+hinge had originally been provided. The break happened to occur so as to
+leave a sufficiently good bearing face at the crown; there was, indeed,
+no tendency for one surface to slide upon another; but in the accidental
+fracture of cast iron this cannot be assured, and the liability to it is
+a risk which should be eliminated if possible.
+
+A second case of very much the same character has also been under the
+author's observation, though in this the ends of the spandrels were not
+built into the brickwork of which the abutments were composed. Other
+instances of fracture either in the arch proper or in the spandrel work,
+have come under notice, though particulars cannot now be adduced; but
+the examples cited are by themselves sufficient to justify the
+conclusion that it is imprudent to construct a cast-iron arch without a
+central pin or its equivalent, unless the abutments, being exceptionally
+well founded, may be relied upon as free from any liability to move. It
+is, however, to be borne in mind that movement in the abutments of a
+small arch of any given absolute amount is more injurious than the same
+amount of movement in the abutments of large arches of similar design,
+so that what may be negligible in the latter case would perhaps be
+destructive in the former.
+
+To the absence of ductility and liability to initial stress must be
+added yet another disadvantage to which cast-iron work is prone--viz.,
+the possibility of concealed defects, blow-holes or cold-shuts; these in
+good foundry practice are not very likely to occur, but, as they are
+possible, cannot be overlooked in considering the suitability of cast
+iron for bridgework, or, indeed, any structural work liable to serious
+stress, and particularly tensile stress. With these remarks by way of
+qualification, the author reiterates his opinion that there is still a
+use for cast iron in bridgework.
+
+With respect to the repair of cast-iron bridges, but little is to be
+said; the possibilities in this direction are very limited. Occasionally
+it may be desired to deal with the fracture of some member in the
+spandrel bracing of an arch, when it is commonly sufficient, and even
+preferable, to limit the repair work to confining the fractured parts in
+such a way as to prevent displacement.
+
+Rarely it may happen that an arch fractures as a result of settlement,
+or other movement, when, if it is decided that safety of the structure
+is not imperilled, it will in this case also be preferable to confine
+the parts simply by flitch-plates or other contrivance, with no attempt
+rigidly to make good the break, the consequences of which treatment
+would probably be to induce fracture in some other place. Effective
+strengthening of a cast-iron structure is seldom practicable, though
+something may occasionally be done by the negative process of lightening
+the dead load, or by remodelling the permanent way. Arches may, however,
+be rendered much more reliable by the introduction of suitable bracing
+where this is either wanting or inefficient.
+
+In scheming such additions it is desirable to arrange for as little
+drilling of the old work as is possible; where this cannot be altogether
+avoided, the position of the holes should be carefully chosen with
+regard to the effect they may have upon the strength of the old work.
+
+
+
+
+CHAPTER XIII.
+
+TIMBER BRIDGES.
+
+
+Timber bridges, though probably the most ancient in type, are yet the
+least durable in any particular instance. The perishable nature of the
+material when used for exposed construction renders it peculiarly liable
+to develop defects which quickly put a limit to the life of the
+structure. In addition to decay in the body of the main members--which
+may perhaps be long delayed, so that a simple beam bridge may last for
+many years--there is in more complex designs decay at connections and
+joints, which proves very detrimental to the integrity of the whole.
+Water running upon the surface of a member gravitates to its lower end,
+and, if there be a joint or other connection, settles there, to be
+productive of lasting mischief. From this cause, together with a very
+common deficiency of bearing surface relative to the forces to be met,
+the joints soon develop some movement; working of the structure
+commences under passing loads, its final destruction being then a
+question of time only. Each joint is, in fact, in timber bridge
+construction a source of serious weakness to a degree which has no
+parallel in well-designed metallic bridges.
+
+Wrought-iron straps to confine the ends of raking members, or for other
+uses, are liable to crush into the wood, and bolts are apt to enlarge
+the hole through which they pass. Wood keys, where these are introduced
+to prevent one timber from sliding upon another, are also prone to
+develop cracks in the main members, and fibre crippling from excess of
+stress. All these defects are, however, in timber-work more easily
+defined than efficiently remedied, as it is barely practicable for any
+but the harder woods to ensure, for heavy loads, a sufficiency of
+bearing surfaces.
+
+The most readily detected evidence of deterioration in timber bridges is
+the sag of its bearing members, or trusses, for the simple reason that
+if there is no local trouble at the joints, there will probably be no
+appreciable drop at the centre of the span. The existence of such a
+depression may, however, be caused in rare instances by the spread of
+the supporting piers or abutments, particularly in the case of beams
+trussed by end diagonal rakers and having no tie.
+
+Bridges formed of deep trusses, with the road upon the top, are
+sometimes found to be wanting in lateral bracing, the result of which is
+that the main trusses go out of line, leaning considerably one way or
+the other, being checked only by such rigidity as the joints and
+floor-beam attachments may have, with possibly some assistance from the
+end connections of the span.
+
+The decay of piles where entering the ground or water is, of course, a
+fruitful source of trouble, as also is the sinking of piles, where these
+are insufficient in number, or have not been well driven in the first
+place.
+
+A vital difficulty with timber structures generally is the uncertainty
+that will commonly exist as to how far decay extends in those cases
+where it has started. Timber does not necessarily show upon its surface
+the evidences of internal rotting. Memel timber may, indeed, be
+sometimes found to have become thoroughly unreliable, yet showing no
+sign of this upon its painted surface. By sounding the wood with a
+hammer, or by probing, its condition may commonly be ascertained. In
+cases of doubt, an auger-hole will make it clear as to whether the
+interior be good or otherwise, as to the particular parts tested; but
+only as to those parts, leaving it a matter of guesswork as to the
+remainder.
+
+[Illustration: FIG. 85.]
+
+A railway bridge having many of the defects which have been indicated
+may be quoted as an example. This structure crossed a canal, supported
+upon piles, some of which were in water, others carrying land spans. The
+canal span consisted of four trusses, one under each rail, or nearly so,
+framed in the manner shown in Fig. 85, precise details not, however,
+being now available. The trusses, apart from deflection under live load,
+sagged considerably--in one instance, 4-1/2 inches; one inside truss was
+also leaning towards the centre line of the bridge as much as 3 inches.
+One raker, or diagonal strut, was rotted half through its thickness, and
+many other timbers were badly decayed. The end connections and joints
+were also in a bad condition. The vertical tie-bolts of the main trusses
+were all slack. The piles generally, many of which were badly decayed,
+had sunk and inclined towards one end of the bridge about 4 inches in 7
+feet of height, the ground being soft and unreliable.
+
+Movement under a passenger train crawling over the bridge was very
+appreciable, but not startling. There had been introduced, from time to
+time, additional timbers and iron ties, with the object of rendering the
+spans more reliable, but leaving it somewhat difficult to determine the
+function of the several members. The bridge was, of course,
+reconstructed.
+
+[Illustration: FIG. 86.]
+
+[Illustration: FIG. 87.]
+
+[Illustration: FIG. 88.]
+
+An instance may here be cited showing how badly distorted a timber
+structure may become without actually falling. The bridge referred to
+consisted of three spans of 29 feet, each span having two trusses,
+between which ran a colliery tramroad, 1-foot 6-inch gauge; the corves
+running upon this, at 4 feet 6 inch centres, weighed, when full, about
+10 cwt. each. The trusses were badly out of shape, the centre span
+having sagged 5-1/2 inches, with one truss of the same span nearly 10
+inches out of line at the centre. This little bridge, of which some
+details are shown in Figs. 86, 87, and 88, had been in use about twenty
+years.
+
+[Illustration: FIG. 89.]
+
+A third case which may be named is that of a road bridge, about 12 feet
+wide, crossing by thirteen spans a shallow river liable to floods. The
+construction was of a simple character, as indicated in Fig. 89, and
+consisted of piles supporting trussed beams, which had sagged in some
+instances over 2-1/2 inches. The bridge had, some years previous to the
+author's inspection, been heavily repaired, many new strut and
+stretching pieces having been introduced, the piles also being
+reinforced or renewed. Five years before, a traction engine, said to
+weigh 5 tons, had passed across the bridge in safety; but the author
+noticed that a coal wagon, which, with the horse, weighed about 50 cwt.,
+when walked slowly over set up much movement. This bridge had been in
+use nearly thirty years, and was very much out of line from end to end.
+
+Though timber bridges cannot at the best be considered durable, yet, by
+attention to certain points in design and construction, their length of
+life may be materially enhanced. Every cut across the grain may be
+considered an element of weakness by exposing the material to quicker
+decay, for which reason the number of ends, or of joints, should be
+reduced to a minimum. An additional reason for reducing the number of
+joints or other connections is the liability of these to develop
+movement, as already stated, the yield of any one joint, being the cause
+of movement in others, which might, but for this, have remained close.
+These considerations lead to the conclusion that fewness of parts is, in
+timber construction, as in structural work generally, an excellent
+principle to observe. Mortising, elaborate scarf joints, recessing, or
+any cutting into the timber which is not essential, should be avoided,
+the simplest forms of connection being preferable, if at all suitable.
+If a step or butt surface is wanted for any member, it is commonly
+better to provide this by a cleat or other added piece, rather than by
+cutting into the timber butted against.
+
+A complicated joint formed in the body of main timbers can only be
+renewed by renewal of the timber itself, whereas by the method indicated
+the joint is readily tightened, or re-made, without involving the main
+member. Bearing surfaces should be ample, straps of liberal dimensions,
+and bolts large (with good washers), both for the sake of bearing
+surface in the holes, and reduction of any liability to bend under
+cross-stress. In trusses of the form shown in Figs. 85 and 86, it is
+desirable to introduce diagonal members in the middle bay, even though
+it may appear that the stiffness of the main beams is sufficient to
+render this unnecessary as a matter of strength, as without these there
+is apt to be, under rolling load, a slight distortion, leading to
+working of the joints and free entry of moisture. Lateral bracings
+should also, for much the same reasons, be introduced, even though they
+may not appear necessary in the new structure, with joints all close and
+effective.
+
+Projecting ends of timbers should be carried out well beyond the
+requirement of strength or bearing, in order to ensure a liberal margin
+for that decay in the end fibres which commonly develops. Timbers
+resting upon abutments, or running into confined spaces, should be
+arranged for free ventilation and ready drying. Occasionally joints at
+the lower ends of timbers are protected by lead or zinc flashings to
+prevent water running into them, a method which should have some
+protective value. Whatever measures may be adopted, whether in the
+design or execution of timber bridge-work, will, however, be but little
+effective, if the timber itself is not good of its kind, and well
+seasoned.
+
+Creosoting to be useful should be thorough and something more than skin
+deep. The timber itself should be well dried before treatment.
+
+The repair of timber bridges very largely consists in the renewal of
+decaying timbers, where this is practicable, or in adding supplementary
+pieces where the old cannot conveniently be displaced. Joints may be
+tightened up by hard-wood wedges, properly secured to prevent slacking
+back, all bolts being also screwed up tight, perhaps some additional
+being introduced.
+
+Piles standing in water, which have decayed, may be strengthened by
+driving other piles between the old, or on either side, but not of
+necessity opposite to them, and by means of waling timbers bolted to the
+old piles, put in a position to take load, either by the walings resting
+upon their tops, or being bolted to them. Piles decayed where entering
+solid ground may generally be strengthened by bolting on supplementary
+timbers to reach well above and below the decayed part, or by cutting
+out the bad length, introducing a new piece, and fishing the butt-joints
+in a proper manner. But all remedial measures have generally to be
+considered with reference to cost, as compared with the probable
+increase of life of the structure. With a bridge in an advanced state of
+decrepitude, such repairs may prove anything but economical, and at the
+best defer reconstruction but a very moderate length of time.
+
+
+
+
+CHAPTER XIV.
+
+MASONRY BRIDGES.
+
+
+Masonry bridges, in which description it is intended to include
+structures both in stone and brick, are, when well built, amongst the
+most durable and long-suffering of any which come under the care of a
+maintenance engineer; yet when developing the faults peculiar to their
+kind, they may be the occasion of much anxiety, and render necessary
+frequent inspection, or even continuous watching.
+
+Apart from decay of mortar or material, defects may very commonly be
+traced to the foundations, or to earth-slips. Sinking, when uniform, may
+be quite harmless, though possibly inconvenient; irregular sinking of
+piers or abutments is quite a different matter. It is, however,
+remarkable to what a degree sinking may be evident, without of necessity
+rendering a structure unsafe. Movement of an amount and kind which would
+be fatal to the connections of metallic bridgework is endured by bridges
+of stone or brick; not, it may be, without damage, yet with no occasion
+for alarm. The superstructure of metallic bridges may often, however, be
+restored to the true level before the mischief has become serious,
+whereas in the case of masonry arches this is not practicable.
+
+Spreading of the abutments is very seldom the cause of any great injury
+to an arch, though it is common enough to find old and flat arches
+slightly down at the crown; but the contrary case of abutments closing
+in is not very unusual when these are high, or terminate a viaduct over
+a deep valley. Such an abutment may move during or soon after
+construction, throwing up the crown of the end span affected; or, if the
+arches are very solid and heavy, the abutment may slide forward at the
+base, with no sensible reduction of the opening.
+
+When a viaduct connects the two ends of a high embankment, it may happen
+that the end piers are not clear of the embankment slope, in which event
+a pier may, should the bank slip, move with it, as to that part not in
+solid ground; with the result, in a bad case, that it is broken across
+and the superstructure imperilled.
+
+[Illustration: FIG. 90.]
+
+A case of abutment movement is illustrated in Fig. 90, which represents
+the end arch of a masonry viaduct, one abutment of which had moved
+forward in the manner already referred to. From the springing upwards
+the arch retained its form to within a short distance of the crown,
+where it was forced up in the way indicated. When the movement became
+pronounced, heavy timber centering was introduced, with the object of
+preventing any mishap, the damaged portions being ultimately cut out and
+made good. The structure was thirty-five years old.
+
+The practical utility of stop piers in long arched viaducts is, perhaps,
+rather in checking movement of the tops of piers under moving load than
+in arresting actual failure of a series of arches. That the tops of
+piers do move very sensibly need not be doubted. The author has
+attempted to measure this in the case of piers about 60 feet to the
+springing, by means of a theodolite placed below, but has reached no
+more definite result than that a movement existed, of which he was not
+able to determine the amount. If in a viaduct some arches are more
+heavily loaded than others, each spreading slightly, the end piers of
+the group will move amounts which together equal the sum of the
+individual span spreads, with a tendency in the arches beyond those of
+the group overloaded to rise.
+
+This rocking may be detrimental both to the piers and arches, and helps
+to account for the disintegration of mortar in arches and piers, which
+not infrequently happens. The soffits will sometimes be seen with a
+thick incrustation of lime, which has washed out of the joints, or from
+limestone ballast above, where this has been in use. Arches of tall
+viaducts may, indeed, become in so bad a condition that pieces of stone
+or brick will drop out, necessitating repair at heavy expense, of which
+scaffolding is commonly a large part.
+
+Tall piers may be found badly out of the upright due to sinking of
+foundations. A marked case of this kind came under the author's
+notice--a viaduct of fifteen semicircular arches, in which, though many
+piers were wanting in truth, one in particular was about 1 foot 4 inches
+out of vertical, making one side of the shaft plumb, and doubling the
+normal batter of the other. Inquiry showed that in this instance the
+pier had never been upright from its earliest history dating back
+thirty-six years. This makes clear the desirability, to avoid hasty
+conclusions, of ascertaining, when it is possible to do so, the complete
+record of any structure.
+
+A bridge fifty-eight years old, of three skew spans, carrying a railway
+over a canal, and having somewhat flat brick arches with stone quoins
+upon low piers, developed the somewhat unusual defect, as to the centre
+arch, of splitting along its length for about 10 feet, parallel to and
+some 7 feet from one face. In this case there was reason to believe that
+there had been considerable local settlement of the piers on that side
+of the bridge. The arches were otherwise in bad condition, the brickwork
+poor, and the mortar decayed. Each arch was down at the centre, and
+displayed a fault not unusual where bad brickwork joins up to good cut
+stonework, the quoins showing a tendency to separate from the brick
+rings. Below the bridge were coal-workings.
+
+Brick arches built in parallel rings sometimes separate one ring from
+the other, demonstrating the known propriety of bonding the rings
+together properly, and of carrying the arch round, when building, at its
+full thickness.
+
+[Illustration: FIG. 91.]
+
+An instance of bridge failure from a somewhat peculiar cause may be
+quoted as of some interest, largely because the structure was very
+ancient, having been in existence some 400 years. This bridge, carrying
+a road, was of the type usual in old masonry bridges over a river,
+having small arches, thick piers, and solid backings to the arches. Two
+flood-openings at one end had, by sinking and want of care, become
+partly closed. The centre arch had, however, been widened about 140
+years previously. During a severe flood, the swollen river, overflowing
+its banks, trespassed upon a timber yard a little above bridge, and
+washed down into the stream a large quantity of sawn timber; this,
+unable to get through the main arch with freedom, compacted into a
+serious obstruction. The flood water, thus checked in its passage, seems
+to have scoured below the timber, and robbed the piers of such support
+as they formerly had (see Fig. 91). The bridge stood in this condition
+till the water lowered, when the middle part of the structure broke up,
+and subsided into the hole which had been washed out. But for the
+monolithic character of the old work it is probable the bridge would
+have failed long before, as the gravel bed on which the piers stood had
+been partly undermined for very many years. The case is instructive, as
+showing how a slight accident--powerless by itself to work mischief--may
+be very damaging when allied with so powerful an agent as running water.
+
+[Illustration: FIG. 92.]
+
+The enduring character of even the roughest class of masonry arch, if
+only the material be good and abutments stable, is shown when it becomes
+necessary to destroy old work of this character. Fig. 92 represents a
+short length of "cut and cover" arching in process of demolition, just
+before it fell in. The masonry was of hard sandstone rubble and had been
+cut away, as shown, till at the point A only a very small piece of the
+arch remained, when the length finally broke up and dropped. Arches have
+commonly a great reserve of strength; tunnel linings are, indeed, often
+badly out of shape, closed in, and sunken; yet continue, with close
+watching, and occasional repairs where the work has decayed or bulged,
+to serve the purpose intended.
+
+Though the equilibrium of masonry arches has been the occasion of much
+profound study, and the nicest calculation has sometimes been applied to
+the design of such work, yet it appears that when an arch is well backed
+up, the theoretical linear arch need have but little connection with the
+figure of the intrados; a statement consonant both with common-sense and
+the teachings of experience. With solid backing, this would indeed seem
+to be more important than any part of the arch ring below the top of the
+backing, the lower part of the ring serving chiefly to preserve the face
+of the solid work. Arches are frequently to be met with so out of their
+true shape that but for the consideration named, failure would seem to
+be inevitable. The masonry or brickwork does not always show evidence of
+damage, if the distortion has been slow; suggesting that structures of
+this kind have a power of accommodation with which they are not
+generally credited.
+
+A noticeable cause of deterioration of masonry structures, which may be
+quite independent of settlement, is serious vibration. This is well
+known in connection with church belfries, and is also locally apparent
+when telegraph or other poles are attached to masonry parapets.
+Vibration, when caused by heavy railway traffic, acting upon arches
+light or originally bad, may demoralise the structure to such an extent
+that repair becomes exceedingly difficult, because of the extensive
+character of the mischief; but masonry bridges substantially built, and
+particularly those carrying ordinary roads, and not subject to much
+vibration, have great lasting powers, if repaired with skill, or even
+let alone. Distortion of the arch may be quite consistent with practical
+stability, if the movement or decay with which it originated is not
+progressive, or has been arrested. In this connection a distinction is
+to be made between arches well backed, to which the foregoing remarks
+apply, and in which the two halves of each arch may act as separate
+monoliths meeting at the crown, and the case of a true arch ring
+independent of any outside resistance, such as backing or spandrels may
+give, and depending almost wholly upon the proper balance of its
+component voussoirs for its stability. With the latter class of
+structure no liberties may be taken; whilst with the former there is
+seldom cause for fear, if the foundations do not give way, and the work
+is dealt with judiciously, if at all. It must, however, be understood
+that there are limits as to what may be done effectively, short of
+rebuilding, in dealing with structures in which, perhaps, brickwork is
+rotten and mortar decayed and crumbling, the whole being little better
+than a broken mass of rubbish.
+
+In cases where it may be prudent to introduce safety centring, as in an
+instance already referred to, it is commonly expedient to refrain from
+causing this to take any sensible part of the load till all movement has
+ceased, the centres being at the outset largely precautionary. The
+requirement with an arch in bad condition is to avoid disturbing it for
+the worse. If the centres are wedged up whilst movement is still going
+on, the effect may be to cause the arch to break up upon the centring,
+and precipitate repair work which might otherwise have been left to a
+more convenient time, when all movement had stopped or been checked by
+suitable measures. Viaduct arches in a bad condition, but not
+necessitating the use of relief centres, are commonly dealt with
+piecemeal by cutting out the bad places, a small part at a time, and
+making good. The work requires the greatest care of experienced men.
+
+Pointing masonry or brickwork is effective for little other than
+protective purposes, and to check further weathering; it has obviously
+no effect upon the interior work, and if made to cover up the evidences
+of internal decay, is even misleading and objectionable. In extreme
+cases it may be desirable to open out the road and deal with the
+filling, to relieve or to strengthen the outer spandrel walls, which
+sometimes bulge, or for other purposes, as, for example, for rebuilding
+inner spandrel walls, grouting up or otherwise repairing solid backing,
+in which operations some regard must be had to the effect of the work
+upon the balance of the opposing halves of the arch.
+
+Of the different classes of masonry commonly used in bridgework, it may
+be well to remark that good coursed rubble, or preferably that variety
+bonding both vertically and horizontally, of a durable stone, perhaps
+quite unfit for any but rough dressing, may make a most lasting
+structure, the mortar, of course, being good. Each rough-dressed stone
+presents a durable piece, fragments removed separate from the block,
+probably along some line of relative weakness--there is no "nursing" of
+weak corners; whereas with stones reduced to a perfectly regular shape
+by chisel work, the plane surfaces and geometrical angles are made with
+partial regard only to the natural grain of the stone.
+
+
+
+
+CHAPTER XV.
+
+LIFE OF BRIDGES--RELATIVE MERITS.
+
+
+The life of bridges of differing materials has been incidentally touched
+upon by the examples quoted, in dealing with each class of structure. It
+will be useful to recapitulate some of the facts adduced, and to compare
+the terms of life so far as they appear to be indicated; but in doing
+this it is necessary to remember that the life of a bridge of any one
+material is inseparably connected with its own private history. The
+duration of any such structure may be limited by adverse conditions,
+peculiar to the case considered, by defects of design, material, or
+workmanship--present from the first--or by neglect, overloading, or
+accident, making up its later record.
+
+With the exception of timber structures, it is difficult to find any
+class of bridges furnishing examples which have reached the limit of
+life, independently of the evils named, and as a result of unavoidable
+decrepitude. There are none the less influences at work tending to this
+condition, and which it is too much to expect can in all cases be
+foreseen or completely guarded against, such as the shifting or scouring
+of river-beds, settlement of foundations, natural decay, and minor
+faults in design, which even in the most capable hands may be expected
+ever to fall short of perfection. At the best, then, the life of any
+structure, though long, must have a limit. With bridges of more average
+or inferior qualities the life may be positively short, even without the
+destructive influence of overloading.
+
+Dealing with instances of metallic bridges, the adjacent table gives the
+time each had been in existence when removed, and some indication of the
+reason for its condemnation. Those marked with an asterisk were cases of
+pronounced high stress. From a study of the table it appears that in
+actual practice, making no excuses of any sort, the length of life of
+the wrought-iron bridges specified varied between twelve and thirty-six
+years; but these figures applied to this collection of cases only. It is
+to be remarked that many other bridges outlasted these, and are likely
+to continue reliable. These results show, then, no more than that some
+wrought-iron bridges are short-lived, having, in fact, been selected as
+examples of this. Longer-lived exceptions are useful, as indicating that
+the durability of such structures is by no means so limited as the table
+would suggest. It is to be observed that, as design and maintenance are
+now better and more generally understood than when experience was
+largely wanting, it is to be expected that later examples will show no
+such poor results.
+
+Of steel bridges little can be said, because of the limited time this
+material has been in use; but the generally acknowledged belief, quite
+in agreement with the author's observation, that steel rusts more freely
+than wrought iron, suggests that such bridges will have a shorter lease
+of life, the more so that the surface-to-section ratio is also greater
+for higher unit stresses, though other adverse influences are much the
+same for one material as for the other.
+
+Of cast-iron structures but few cases have been given; of these,
+cast-iron arches have been noticed as developing defects which led to
+reconstruction, or to limiting the loads to be carried. Plain cast-iron
+girders, on the other hand, have never, under the author's direct
+observation, been removed for any other reason than because they were
+cast iron, or from over-stress, due to the growth of loads; never from
+defects or wasting, though it is not suggested no such cases exist. The
+author has no evidence which points to what may be the limit of life of
+a good cast-iron girder fairly treated.
+
+_Examples of Life of Metallic Bridges._
+
+  -------------------------+-------+------+----------------+------------
+        Description.       | Span. | Age. |   Defect.      | Reference.
+  -------------------------+-------+------+----------------+------------
+                           |ft. in.|Years.|                |
+                           |       |      |                |
+                                _Wrought Iron._
+                           |       |      |                |
+  Plate girders            |  (?)  |  12  |Loose rivets    |
+    *Ditto                 | 35  0 |  12  |Ditto           |p. 52
+     Ditto                 | 55  0 |  14  |Rust. Distortion|pp. 78 & 97
+  Trough girders           | 11  0 |  16  |Loose rivets.   |p. 50
+                           |       |      |Cracked webs    |
+  Plate girders            |  (?)  |  22  |Loose rivets    |
+  Twin girders             | 31  6 |  23  |Weak. Cracked   |p. 13
+                           |       |      |webs            |
+     Ditto                 | 35  6 |  23  |Weak. Distorted.|p. 74
+  Plate girders            | 42  0 |  23  |Loose rivets.   |p. 21
+                           |       |      |Cracked webs    |
+     Ditto                 | 72  0 |  29  |Weak. Loose     |p. 53
+                           |       |      |rivets          |
+     Ditto                 | 47  0 |  24  |Distortion      |p. 9
+     Ditto                 | 32  0 |  32  |Rust. Cracked   |p. 14
+                           |       |      |webs            |
+    *Ditto                 | 25  0 |  36  |Weak            |p. 63
+                           |       |      |                |
+                                  _Steel._
+                           |       |      |                |
+  *Trough girders          | 15  8 |  32  |Weak. Rusted    |pp. 68 & 98
+                           |       |      |                |
+                                _Cast Iron._
+                           |       |      |                |
+  *Girders                 | 32  0 |  36  |Weak            |p. 141
+   Girders, cast-iron piles|  (?)  |  44  |Ditto           |
+   Arches                  | 45  0 |  55  |Crack. Settle-  |p. 145
+                           |       |      |ment            |
+     Ditto                 |100  0 |  62  |Crack. Deforma- |pp. 80 & 145
+                           |       |      |tion            |
+  -------------------------+-------+------+----------------+------------
+
+With timber bridges the length of life appears to be about twenty-five
+years, but this is very largely dependent upon the question of
+maintenance, and may range from fifteen to thirty-five years. It is
+manifest that repairs, when extensive and consisting of the renewal of
+the more essential parts of the structure, border upon reconstruction,
+and may be continued indefinitely. The length of life in ordinary cases,
+and for the timbers commonly used in this country, may, for railway
+bridges, be taken as stated, though for highway bridges possibly longer.
+
+Of masonry bridges little is to be said but that it is only in cases of
+bad work or material--with, perhaps, vibration or settlement--that these
+have a shortness of life comparable with that of defective metallic
+bridges. Where these adverse conditions obtain, heavy repairs may be
+necessary before the structure is many years old; but, under reasonably
+fair conditions, bridges of masonry may be expected to outlast
+structures in any other material. Apart from road-bridges which are
+admittedly long-lived, there are a large number of railway bridges and
+viaducts of masonry which, despite heavy loads and vibration, have been
+in use for the past seventy years.
+
+Dealing with the cost of maintenance, this with bridges of wrought iron
+or steel should result simply from scraping and painting, with such
+other incidental work as may be necessary on the subsidiary materials
+used in the structure. The cost of painting will vary with the height
+and character of the bridge, and the amount of scaffolding, if any, and
+may be from 5_d_. to 1_s_. or more per square yard; this if distributed
+over five years, a not unusual interval between each painting, works out
+at an appreciable figure, which may vary from one-third to one per cent.
+of the first cost, per annum. The yearly cost of painting steel-work
+will, for shorter intervals, come to a somewhat higher figure. Serious
+occasional items of expense are those which should not be necessary,
+repairs and possibly strengthening, which may raise the total cost of
+maintenance very considerably.
+
+Cast-iron bridges, being less liable to rust, cost less for painting
+than other metallic bridges; and if the cast iron is closed in by
+masonry, practically nothing; they do, indeed, involve very little
+expenditure in the maintenance. Not being very amenable to repair or
+strengthening, cast-iron bridges commonly remain very much as built, or
+are reconstructed.
+
+The proper care of timber bridges may become costly as the structure
+gains in age, and soon grow to a very wasteful expenditure. This is
+evident when it is considered that repairs may be necessary after ten
+years, and that whatever may have been the cost of any part when new, it
+cannot be replaced for the same amount, having regard to the labour
+expended in removing the old member, and the special precautions to be
+observed in dealing with an old structure carrying its load. In addition
+to ordinary repairs, there will be paint or other protective coating to
+be applied, though this is not always done.
+
+The upkeep charges of masonry bridges will be practically nothing in
+favourable cases; but, on the other hand, where extensive repairs become
+necessary, may reach a considerable amount. Exceptional outlays are,
+however, infrequent, and may be spread over a large number of years, in
+those rare instances in which they become imperative.
+
+  _Durability._      _Maintenance     _First Cost._
+                     Charges._
+
+  Masonry            Masonry          Timber
+  Cast Iron          Cast iron        Masonry
+  Wrought iron       Wrought iron     Steel
+  Steel              Steel            Cast iron
+  Timber             Timber           Wrought iron
+
+For purposes of ready comparison, placing bridges of the materials under
+review in order of durability, they would appear as in column 1 of the
+table above; in order of low maintenance charges, generally as in column
+2; and in order of low first cost, as in column 3. With respect to the
+question of first cost, the arrangement of the third column applies only
+to small bridges, say, up to 70-foot span; and, being liable to
+variation with the conditions, is but approximately correct. The less
+costly descriptions of masonry are alone considered in this connection.
+
+It may be added that the total yearly charge of interest on first cost,
+redemption, and maintenance, appears to be for masonry bridges, about
+one-half only of the corresponding totals for bridges of wrought iron,
+steel, or timber; those of cast iron taking an intermediate place.
+
+Summarising the above considerations, and dealing with the relative
+merits of bridges in the different materials, it may be broadly stated
+that for conditions at all suitable nothing seems to be superior to
+masonry--including in this description first-class brickwork--whether
+for road or railway bridges. One pronounced advantage of such bridges
+with respect to length of life, is that they are but little affected by
+increase of loads. The mass of a masonry arched structure is so great,
+and the margin of strength commonly so liberal, that considerable
+increments of load may have but little effect upon the reliability of
+the structure.
+
+Cast iron has, for bridges of simple design, a strong claim to the
+second place, though its want of ductility is a demerit. It can,
+however, have but a limited use in bridge construction, being applicable
+only to small girder spans and skilfully-designed arched structures.
+
+For bridges of moderate span in which the question of cost does not
+control the matter, wrought iron should probably come next, steel being
+best reserved for those of a larger size, in which weight of the
+structure greatly affects economy.
+
+Timber may be regarded as a material rarely to be used in this country
+for structures to occupy a permanent place, unless for urgent economic
+reasons of the moment.
+
+While expressing this general view of the matter, it is to be admitted
+that the propriety of these conclusions is somewhat discounted by the
+difficulty there now is in obtaining cast iron of the desired
+toughness, or wrought iron with promptitude and sufficient variety of
+section at a reasonable price.
+
+It is apparent, also, that the choice of material may be largely
+influenced--even determined--by considerations of headway, construction
+depth, or character of foundations; so that no very definite rules can
+be usefully laid down, though the adoption of unsuitable materials has
+not been so unusual as to make these suggestions altogether
+purposeless.
+
+
+
+
+CHAPTER XVI.
+
+RECONSTRUCTION AND WIDENING--CONCLUSION.
+
+
+The need for the reconstruction of bridges, arising from various causes
+which have been treated in the preceding chapters, original weakness or
+faults in design, decay or defects, may also be caused by such
+extraneous considerations as the growth of loads, widening of the
+openings spanned, or improvement of the headway.
+
+In any case, a precise survey or measuring up of the structure and its
+immediate surroundings is required, in the execution of which the
+greatest care is desirable, and with respect to which it may be well to
+give a few hints.
+
+The surveying chain, when used, should be tested, the measure of
+accuracy required rendering this imperative in a degree peculiar to work
+of this class. Linen tapes should also be compared with a reliable steel
+tape, and used only where sufficiently accurate for the particular
+purpose. A careful and observant man may do very good work with a linen
+tape, making just that allowance in the sag of the tape which corrects
+for the inevitable stretch; but there is still some uncertainty involved
+in its use, and the author prefers to rely upon a steel tape,
+notwithstanding the inconvenience commonly experienced from its
+intractable nature and liability to damage.
+
+Instruments used must also be in the best adjustment; as errors, which
+in ordinary field work may not be of great importance, are inadmissible
+in bridge work.
+
+It is not necessary here to enter upon the methods of small survey
+work, but it may be desirable to point out that abutment walls should be
+plumbed for verticality; girders, which are liable to be leaning,
+defined in position by reference to their bearings; and generally that
+it should never be taken for granted that there is truth in old work, or
+that this may be assumed as to line or level.
+
+In cases where disputes with any local authority as to headway are
+likely to arise, it is prudent to supplement the information as to level
+of soffits by rods cut to length in strict agreement with the clear
+height, before removing the old superstructure.
+
+It is apparent that in cases where the superstructure is already
+condemned, the detail measurements may be confined to that part of the
+structure which is to remain, securing only such information as to the
+work superseded which may be required in arranging for the new work.
+
+In taking particulars of skew bridges, needless as the warning may seem,
+it is yet necessary to remark that there may be right or left-hand skews
+which will not reverse. The author has known a disregard of this to make
+serious trouble in two instances.
+
+Dealing first with reconstruction of the superstructure of railway
+under-bridges, these, if small, may not give much trouble, though the
+demand for greater strength will, perhaps, involve some difficulty in
+working to the limiting construction depth--i.e., the distance from the
+top of rail to soffit of bridge--particularly as many old bridges have a
+very niggardly allowance in this respect. It may be, and quite commonly
+is, necessary to raise the rails a small amount, or, if headway is not
+restricted, to lower the soffit. Clearances between the running gauge
+and girder-work may also be difficult to secure, more liberal allowances
+being now required than formerly. Complications in the character of the
+permanent way, so frequently found upon old bridges, should, of course,
+be got rid of, if possible; but the endeavour may introduce further
+difficulties. Regard must throughout be had to the methods to be adopted
+in removing old work and in erecting the new. Perhaps the simplest case
+to deal with is that where girders lie parallel to, and under the rails,
+with a timber floor upon which the permanent way is carried, as sections
+of the road involving pairs of girders may be readily removed, and
+replaced by the new girder-work (see Fig. 93). If the deck be of trough
+flooring or old rails, the matter may not be so simple, as regard must
+then be had to the position of joints in the existing floor, and the new
+work be schemed with respect to the number and office of girders which
+may be got in at any one breaking of the road. A slight slewing of rails
+may sometimes be resorted to on occasion, where this has the effect of
+releasing some part of the work not otherwise to be dealt with.
+
+[Illustration: FIGS. 93 and 94.]
+
+Bridges having main girders, with timber or trough flooring resting upon
+the bottom flanges, or suspended by bolts, will, if carrying many roads,
+cause some little difficulty, as the dismantling of any one span
+involves the disturbance of others; where, however, many lines are
+concerned, it may be feasible to put one or more temporarily out of use,
+preserving the continuity of traffic over those which remain, but
+refraining from any diversion of the more important roads.
+
+Somewhat similar troubles occur where main girders with cross-girders at
+the lower flanges are found, particularly if the cross-girders are
+arranged in line, the ends abutting on each side of the same main girder
+webs. It is seldom, however, that this construction is used in bridges
+of small span carrying many roads; but where it does occur, it may
+necessitate the use of timbering below, to carry the ends of
+cross-girders when freed from their supporting main girders. (See Fig.
+94.)
+
+[Illustration: FIG. 95.]
+
+If it is proposed to use new main and cross-girders, it is desirable to
+arrange these in the manner already recommended, the cross-girders not
+in line; this has peculiar advantages in reconstruction work, as the
+bolting up and riveting of the cross-girder ends is not hampered by
+other cross-girder attachments, leaving each piece of floor complete in
+itself. Twin main girders are occasionally used with the same object,
+and present the advantage of simplicity in erection and independence of
+one span from those adjoining (see Fig. 95); but the method is wasteful
+of space, and involves a somewhat greater total weight in the main
+girders.
+
+The foregoing observations apply more generally to small single-span
+bridges, the operations on which may be effected without any material
+disturbance of traffic arrangements; though this can seldom be wholly
+avoided, it should be confined, where practicable, to a few hours on a
+Sunday.
+
+The reconstruction of bridges over 70-feet span may have to be dealt
+with under more elaborate arrangements, if carrying two lines only,
+possibly with single-line working for a period more or less protracted;
+or it may be necessary, having regard to the weight of main girders to
+be removed, to carry the whole structure upon temporary staging,
+supporting the road independently, cutting up and removing the old work,
+and later putting the new work in place, either by detailed erection in
+its ultimate position, or by erection at one side and drawing across.
+The latter method is, however, commonly reserved for cases in which no
+special staging is used under the old structure.
+
+Bridges of a number of openings are usually dealt with by securing full
+possession of one road at a time, which for double-line bridges
+necessitates single-line working. It is commonly out of the question,
+even with moderate spans, to deal with some of these only at a time, and
+so avoid continuous possession of one road, for a lengthened period; and
+it can only, as a rule, be managed where the ends of the new main
+girders do not in any way interfere with those of the old, and where it
+is not necessary to reset bed-stones, or make other alterations in the
+bearings which necessitate the complete clearance of the pier-tops. In
+exceptional cases it may be found possible to arrange for the complete
+removal of a small number of moderate spans on a Sunday, and the putting
+in place of the new work, as in the case of small single spans.
+
+Spans erected to one side of the final position, to be later travelled
+across, are commonly mounted upon gantry staging, and up to 50 tons
+weight may rest directly upon rails well greased. The power adopted to
+move the span is usually that of screw or hydraulic jacks, or
+occasionally engine haulage, special tackle being in that case necessary
+to apply the engine power in the right direction. If the time is
+limited, or weight considerable, a more elaborate arrangement by which
+the load is supported upon wheels, may be necessary, with a view to
+reducing the resistance to a manageable amount. All work which it is
+possible to do before shifting into place, including the permanent way,
+where this is of a special character, should be executed in advance,
+leaving only the rail connections to be made good when the span is in
+position.
+
+Where timber staging is used to carry the permanent way before
+dismantling an old structure, it is convenient to begin by placing stout
+balks of timber under the sleepers from end to end of the bridge, or
+directly under the rails if space is limited; the staging is then
+arranged to give support to the running timbers.
+
+Metallic under-bridges of ample headway, perhaps over coal-workings
+(since settled down), or for some less sufficient reason made of metal,
+may be cheaply replaced by brick arches built below the old
+superstructure, the springings of the arch being checked into the face
+of the existing abutments. With stout walls, careful work and good
+material will make this an efficient and durable job.
+
+It being a primary condition of reconstruction work to interfere but
+little with ordinary traffic arrangements, single-line working is
+avoided wherever practicable; as this, always objectionable, may
+necessitate the erection of special signals and signal apparatus,
+besides the temporary remodelling of the roads, and in this country may
+involve also a Board of Trade inspection--altogether a troublesome and
+expensive business.
+
+Any bridgework which is accompanied by breaking or blocking the road can
+only be undertaken by arrangement with the traffic department, after
+notice duly given and published in the periodical record of such
+matters; it is generally fixed for a Sunday. Preparatory to this, it is
+necessary to make all ready by getting as much done beforehand as is
+possible. Wherever practicable and prudent, the whole work is released
+from its surroundings, masonry cut away, rivets cut out and replaced by
+good bolts, nuts removed from holding down bolts, or the bolts cut
+through, etc. Particular care should be exercised to ascertain what
+remains to be done immediately prior to removal. It is necessary further
+to arrange for trucks to be in readiness to receive old material, and
+others containing new girder work to be conveniently stationed, having
+been loaded up to come right end foremost; engine power, cranes, empty
+and loaded trucks, being all marshalled and so placed as to be available
+in proper order, and as wanted. There must be no mistake as to what
+roads will be fouled by swinging the crane with its load, or as to the
+reach of the crane in effecting its work.
+
+The whole operation to be conducted on any Sunday should be well within
+the resources of the men and plant engaged in it, or so managed that it
+is a matter of no serious importance if the whole cannot be completed as
+originally desired.
+
+Possession of the roads to be blocked having been secured between
+certain hours, if some part only of the work to be carried out has been
+completed as the time grows short, any attempt to execute the remainder
+may result in checking trains until such time as the line may be
+reported clear--a contingency to be avoided--though the temptation to
+save another Sunday's work by delay of a few minutes to some one train
+may be considerable.
+
+In scheming any reconstruction, it may be insisted that at least one
+feasible method of carrying out the work must be secured, though it is
+the author's experience that frequently some other method than that
+contemplated is in the end adopted, when, some months later, the final
+arrangements for fixing are made. The tendency of a zealous erector is
+commonly to take full advantage of any facilities offered, with a view
+to a moderate amount of work being done at any one time, and to achieve
+as much more as he can himself secure by scheming, or a liberal use of
+labour; all Sunday work, with attendance of engines and cranes, being of
+necessity expensive.
+
+Railway over-bridges do not commonly present any particular
+difficulties. The spans to be dealt with are usually small, and the
+weights to be lifted moderate. The height above rails may, however, be
+above the lift of any crane; and, for the purpose of raising main
+girders, a derrick may become necessary, the rearing and guying of which
+may block many roads during the time it is in use. The girders of larger
+spans, too unmanageable to be lifted whole, may be erected upon staging;
+to secure the requisite headway it may be necessary to build the girders
+at a level above that at which they will finally be, lowering them into
+position when self-supporting, and after the removal of the staging.
+
+The widening of railway under-bridges is, as a rule, a matter of no
+special difficulty, but some remarks may be of use. Widenings should be
+planned with a regard to later reconstruction of the original bridge, if
+that is at all likely to be necessary, and with the object that, when
+complete, the whole should be a consistent piece of work.
+
+It may, indeed, happen that widening of a bridge may involve the
+remodelling or reconstruction of the old work, to enable the new roads
+to be laid down as desired; this is more likely to be necessary where
+there exist main girders not competent to take any additional load, and
+to duplicate which would sacrifice space between the new and old roads;
+or it may be unavoidable because of slewing of the old rails, as part of
+a general rearrangement.
+
+[Illustration: FIG. 96.]
+
+Dealing with widenings simply, there is often some little trouble in
+contriving a connection between the new and the old work, as this may
+have to be made under, or close to, the sleeper ends of the existing
+roads. It is desirable to arrange this part so that no drilling of old
+work for rivets or bolts shall be necessary, there being, in fact, no
+strict connection. By judicious scheming, this may be effected, whilst
+securing freedom from leakage of water at the joint. (See Figs. 96 and
+97.) If tying of the new and old structure is desired, this can usually
+be done quite simply, well below the floor at some more accessible
+level.
+
+[Illustration: FIGS. 97 and 98.]
+
+The strict jointing-up of trough flooring, new to old, at right angles
+to the troughs, cannot be contemplated, but may be dealt with by
+treating each part independently, the ends being near together,
+separated by the space of an inch or so. Each trough end being closed up
+by a diaphragm or oak block to prevent ballast dropping through, the top
+of the space may be covered by a loose strip, secured to prevent it
+shifting, the bottom provided with a gutter of liberal dimensions to
+take away leakage, as it is practically impossible to make this
+arrangement "drop dry" under the conditions common in executing work of
+this kind (see Fig. 98).
+
+[Illustration: FIGS. 99 and 100.]
+
+Where trough flooring, new and old, has to be made good parallel to the
+troughs, the difficulty of making a direct connection is less marked,
+and it is not unusual to introduce a strip cover simply; but if
+accessible, the work is still troublesome, as there is commonly a want
+of strict alignment and truth as to level, between the new and the old
+troughs. It is preferable to arrange for junctions of a more convenient
+type, as in Figs. 99 and 100.
+
+When widening masonry arch bridges by girder-work, it is desirable to
+insure that any girders parallel to the masonry face shall be
+sufficiently far removed from it to enable painting to be executed. The
+space remaining between the girder and the arch may then be bridged by
+floor-plates, or an extension of the timber floor if that is adopted.
+
+In effecting a junction such as this, the author has used the
+arrangement shown in Fig. 101, the advantage being that the piece of
+connecting-floor is sufficiently wide, and also sufficiently flexible,
+to allow the girder-work freedom to deflect without doing harm. The load
+carried by the width of floor is, as to one part, delivered well on to
+the old masonry, in preference to being imposed near to the face. If it
+should for any reason be imperative to place the girder close to the
+arch face, it is preferable to scheme the floor so that there shall be
+no actual contact, the new floor in that case slightly overhanging the
+masonry, as in Fig. 102, or dealt with as in Fig. 103, if depth is
+restricted.
+
+The widening of masonry arch bridges by masonry, calls for no other
+remark than that the new work should be free from the old; though it may
+be advisable, when the widening is narrow, to tie the new work to the
+old in such a way as to permit independent settlement.
+
+If the widening is exceptionally narrow, there may be no choice but to
+bond the new and old work together, and in the best manner, with the
+object of minimising the risk of separation.
+
+[Illustration: FIGS. 101 and 102.]
+
+[Illustration: FIG. 103.]
+
+The above matters relative to widenings, though apparently trifling, may
+by neglect cause much trouble and expense in maintenance. They
+principally concern small bridges, the extension of larger structures
+coming rather in the category of independent works.
+
+
+CONCLUSION.
+
+In bringing these chapters, dealing largely with questions affecting
+maintenance, to a close, it may be well to draw attention to the fact
+that economy in design (apart from improper reduction of sections) goes
+hand-in-hand with economy of upkeep. Given good material, that which
+favours low first cost, simplicity of detail, fewness of parts, absence
+of smithing, the use of rolled sections, and good depth to girders,
+favours also small expenditure in maintenance. The less complex the
+design, the easier will it be to keep the structure in order; the less
+the number of parts, the fewer will be the connections. Freedom from
+smithing eliminates liability to failure at cranks, or other work which
+has been subject to fire. It is apparent also that the free use of
+rolled instead of built-up sections, reduces the liability to trouble
+from bad riveting, or from good riveting overstressed. A liberal depth
+to all girders, by reducing deflections, limits the inclination of the
+ends and gives the connections a better chance of remaining intact.
+Lastly, with work of this character, the labour of scraping and painting
+is simplified and cheapened.
+
+The author wishes to reiterate the statement made in the opening
+paragraphs of this book, that all instances of decrepitude, failure, or
+peculiar behaviour cited, have been under his direct observation. The
+fact is insisted upon simply that the reader may appreciate that the
+information is at first hand.
+
+It has not been thought necessary, nor was it considered desirable, to
+indicate the locality of each case referred to; but it may be said that
+the matter of these chapters has been accumulating during many years,
+and relates to structures under the control of many different bodies.
+
+The study of old bridges is strongly recommended, particularly with
+respect to stress and strain, which in structures new or old, occur
+possibly as may be expected--certainly as they must. Consideration of
+existing work may thus be a useful check upon the fanciful requirements
+of some methods of design. There is a recent tendency, for instance, in
+English practice to over-stiffen the webs of plate-girders, such that if
+the theory upon which the results are based were true, many old bridges
+carrying their loads with no sign of distress, should have failed long
+ago. Excess in riveting is a common extravagance, to which the same
+criticism may in a less degree apply. Considerable impact allowances for
+girders of large span may also be referred to as an application of
+empiric theory not justified by experience, which, as in all cases where
+such considerations fight with facts, should be modified or rejected.
+
+
+
+
+INDEX
+
+
+  Abutments, leaning, 82, 173
+  -- movements of, 158
+  -- settlement of, 78
+  Adjustment of centre girders, 128
+  -- of distributing girders, 120
+  Angular distortions, 88
+  Arches, equilibrium of, 162
+  -- repair of, 163
+  Arrangement of cross girders, 21, 175
+  Asphalt, 26
+
+  Ballast, 29
+  Bearing pressure on rivets, 47, 51, 57
+  Bearings, skew, 4
+  Bottom booms, end bays, 18
+  Bracing, additional, 117
+  -- effects of, 34
+  -- flat bars, 37
+  -- incomplete, 41
+  -- sea piers, 42
+  Bridge floors, 20
+  -- repairs, 107
+  -- surveys, 107
+  Bridges, life of, 165
+  Breaks in [T] bars, 16
+  Buckling of webs, 16
+
+  Camber, 24, 80
+  Cast-iron arches, 80, 145
+  -- -- bridges, 141
+  -- -- columns, 7,144
+  -- -- girders, 141
+  -- -- in sea water, 101
+  Centre girders, 122
+  Cinder ballast, 29
+  Cold-blast iron, 141
+  Cooling stresses in cast iron, 145
+  Construction depth, 173
+  Corrugated sheeting, 29
+  Cost of centre girders, 135
+  -- of maintenance, 168
+  Counterbracing, 19
+  Cracked bedstones, 3
+  -- columns, 7
+  -- web plates, 13, 14, 15, 50
+  Cross girder arrangement, 21
+  -- girders, fixed ends, 22, 118
+  -- -- rusted, 29, 97
+  -- -- weak, 30, 66
+
+  Decay and painting, 96
+  -- of floor plates, 109
+  -- of timber, 28, 150
+  Deflection, 85
+  -- due to booms and web, 86
+  -- exceptional cases, 88
+  -- in new and old work, 85
+  -- working formulae, 87
+  Deformations, 73
+  Depth of girders, 23, 89, 184
+  Diagonal ties, 19, 42
+  Distortion due to temperature changes, 79, 84
+  Distributing girders, 120
+  Drainage holes, 25
+  "Drop" loads, 89
+  Dwarf walls under floors, 26
+
+  Early steel girders, 68
+  Economy, 184
+  Effect of earth slips, 157
+  -- of floor on deflection, 88
+  -- -- -- on stresses, 23, 30
+  -- of high stress, 86
+  -- of permanent way on stresses, 18
+  --of skew on bridge floors, 25
+  -- -- -- on centre girders, 131
+  -- of transverse bracings, 34
+  -- of vibration on masonry, 162
+  -- of wave action on sea piers, 42
+  End bays, bottom booms, 18
+  Equilibrium of masonry arches, 162
+  Examination of bridges, 107
+  Examples of cast-iron bridges overstressed, 141
+  -- of high stress, 70
+  -- of life of bridges, 167
+  -- of rivet stress, 56
+  -- of strengthening, 114
+  -- -- -- by centre girders, 131, 134
+  Excessive bearing pressure, 51
+
+  Faulty workmanship, 80
+  Fixed ends to cross girders, 22, 118
+  Flange stresses, 63, 66, 67
+  Flanges, side loaded, 9, 73
+  Flat bar bracing, 37
+  Flexing of girders, 9, 74, 76
+  Flexure curves, 138
+  Fractured bedstones, 3
+  -- rails, 30
+  -- webs, 13, 14, 15, 50
+  Fractures in cast iron, 7, 145
+
+  Girder bearings, 2
+  Girders on columns, 7
+  -- on masonry, 8
+  Girderwork in masonry, 101
+
+  Headway, 173
+  High stress, 61
+  -- in cast iron, 141
+  -- in rivets, 47, 52
+  Holes for drainage, 25
+
+  Impact, 20, 62
+  Inclination of girder ends, 23, 53
+  Incomplete bracing, 41
+  Initial set, 88
+  Interference with traffic, 177
+
+  Jack arches, 29, 101
+  Joints in rails, 29, 109
+  -- in trough floors, 28, 180
+  Junction between metallic and masonry bridges, 183
+  -- -- new and old masonry bridges, 182
+  -- -- new and old metallic bridges, 180
+
+  Lattice girder stresses, 47-66
+  Liberal depth to girders, 23, 89, 184
+  Life of bridges, 165
+  Limit of elasticity, 61
+  Linen tapes, 172
+  Longitudinal floor girders, 23
+  Loose rivets, 21, 25, 51, 53, 56, 109
+
+  Main girders, 9-17
+  Masonry bridges, 157
+  -- enduring character of, 161
+  Memel timber, 150
+  Methods of calculation, 46, 61
+  -- of observing deflection, 90
+  -- of setting out deflection curves, 138
+  Movements of abutments, 158
+  -- of cast-iron bridge, 82
+  -- of piers, 42, 83, 159
+  -- of rollers, 7
+  -- of wrought-iron bridges, 4, 21, 38, 73
+
+  New members to old work, 116
+
+  Oiling steelwork, 99
+  Old drawings unreliable, 108
+  -- rivets, 21, 51, 54, 55
+  Open webs, 17
+  Overhead bracing, 39
+  -- girders, 118
+
+  Painting, 98
+  Parapets, 79
+  Permissible stress in old work, 110
+  Piers, movements of, 42, 83, 159
+  -- out of plumb, 159
+  Piles, decay of, 102, 150
+  Pitch pine, 28
+  Plasticity, 61
+  Plate webs, 9
+  Plated floors, 23, 25, 30
+  Pointing masonry, 164
+  Proposed rivet stresses, 58
+
+  Quickly applied loads, 89
+
+  Rail joints, 29, 109
+  Rails, breaks in, 30
+  Reaction of cross girder with centre support, 127
+  Red-lead, 98, 100
+  Relative merits of bridges, 169
+  Relief by centre girders, 122
+  Repainting, 100
+  Repair of bridges, 107, 147, 155, 163
+  -- of timber piles, 156
+  Replacing flange plates, 110
+  -- rivets, 111
+  Resistance of cast iron to rust, 101
+  Riveted connections, 45, 86
+  Rivets in cramped positions, 20
+  -- in cross girder ends, 21, 49, 53, 54
+  -- in road bridges, 60
+  -- in webs of main girders, 46
+  -- spacing of, 60, 80
+  -- stresses in, 56
+  Rocking of piers, 8, 83, 159
+  Roller bearings, 7
+  Rubble masonry, 161-164
+  Running load and deflection, 95
+  Rusting, instances of, 29, 96
+  -- of steelwork, 99
+  -- over sea-water, 98
+
+  Sag in timber bridges, 150
+  -- of tapes, 172
+  Scour under piers, 161
+  Sea piers, 42, 102
+  Setting bedstones, 3, 129, 176
+  Settlements, 76, 157
+  Skew bearings, 4
+  -- bridges, right and left, 173
+  -- -- floors, 25
+  Skirting plate, 26
+  Slope of girder ends, 92
+  Softening of cast-iron in sea-water, 101
+  Spacing of rivets, 60, 79
+  Spread of abutments, 157
+  Spring joints, 23
+  Steel trough girders, 68
+  -- troughing, 70
+  Stiffening girders from floor, 12, 40
+  -- to webs, 16, 38, 185
+  Stop piers, 158
+  Strength of light top booms, 40
+  Strengthening of bridges, 107, 122
+  -- bridge floors, 118
+  -- cross girders, 123
+  Stress in plated floors, 31
+  Study of old bridges, 185
+
+  Tall piers, 42, 159
+  Timber bridges, 149
+  -- floors, 27
+  -- staging, 177
+  Top booms, 18
+  Traffic during reconstruction, 177
+  Transverse bracing, 34, 117
+  Trough floors, 27, 180
+  -- girders, 50, 74
+  [T] stiffeners, breaks in, 16
+  Twin girders, 15, 75
+  Twisting of girders, 11, 68, 73
+  -- -- -- corrected, 12
+  Types of reconstruction, 174
+
+  [U]-shaped booms, 18
+  Uncomplicated stress, 62
+  Uniform pressure on bearings, 6
+
+  Value of E in deflection formulae, 87
+  Vibration, 162
+
+  Wasted webs, 14, 29, 96
+  Water, scour of, 161
+  Web buckling, 16
+  -- plates, cracked, 13, 14, 15, 50
+  -- rivets, 46, 50
+  -- stiffening, 16, 38, 185
+  Widening masonry bridges, 182
+  -- metallic bridges, 179
+  Wide spaced rivets, 79
+  Wind pressure, 41, 43
+
+  Yielding of piers, 8, 83, 159
+
+
+  LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
+  GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
+
+
+
+
+Transcriber's Notes:
+
+The text of the original work (including inconsistent spelling,
+hyphenation, formatting etc.) has been retained, except as mentioned
+below.
+
+The slight differences between the Table of Contents and the text have
+not been changed.
+
+Changes made to the text:
+
+Some punctuation errors and obvious typographical errors have been
+corrected silently.
+
+Several illustrations have been moved to where they are described in the
+text.
+
+Page 123, formula (2): the original shows an unclear superscript after
+the first L. As described in the following line of the text, this has
+been changed to L{_l_}.
+
+
+
+
+
+End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe
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